<?xml version='1.0' encoding='utf-8'?>
<FilingSummary>
  <Version>3.25.3</Version>
  <ProcessingTime/>
  <ReportFormat>html</ReportFormat>
  <ContextCount>1064</ContextCount>
  <ElementCount>643</ElementCount>
  <EntityCount>1</EntityCount>
  <FootnotesReported>true</FootnotesReported>
  <SegmentCount>164</SegmentCount>
  <ScenarioCount>0</ScenarioCount>
  <TuplesReported>false</TuplesReported>
  <UnitCount>8</UnitCount>
  <MyReports>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R1.htm</HtmlFileName>
      <LongName>0000001 - Document - Cover Page</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/CoverPage</Role>
      <ShortName>Cover Page</ShortName>
      <MenuCategory>Cover</MenuCategory>
      <Position>1</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R2.htm</HtmlFileName>
      <LongName>9952151 - Statement - Consolidated Balance Sheets</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/ConsolidatedBalanceSheets</Role>
      <ShortName>Consolidated Balance Sheets</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>2</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R3.htm</HtmlFileName>
      <LongName>9952152 - Statement - Consolidated Balance Sheets (Parenthetical)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/ConsolidatedBalanceSheetsParenthetical</Role>
      <ShortName>Consolidated Balance Sheets (Parenthetical)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>3</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R4.htm</HtmlFileName>
      <LongName>9952153 - Statement - Consolidated Balance Sheets (Parenthetical)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/ConsolidatedBalanceSheetsParenthetical_1</Role>
      <ShortName>Consolidated Balance Sheets (Parenthetical)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>4</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R5.htm</HtmlFileName>
      <LongName>9952154 - Statement - Consolidated Statements of Operations</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/ConsolidatedStatementsofOperations</Role>
      <ShortName>Consolidated Statements of Operations</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>5</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R6.htm</HtmlFileName>
      <LongName>9952155 - Statement - Consolidated Statements of Comprehensive Income (Loss)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/ConsolidatedStatementsofComprehensiveIncomeLoss</Role>
      <ShortName>Consolidated Statements of Comprehensive Income (Loss)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>6</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R7.htm</HtmlFileName>
      <LongName>9952156 - Statement - Consolidated Statements of Stockholders' Equity</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/ConsolidatedStatementsofStockholdersEquity</Role>
      <ShortName>Consolidated Statements of Stockholders' Equity</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>7</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R8.htm</HtmlFileName>
      <LongName>9952157 - Statement - Consolidated Statements of Cash Flows</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/ConsolidatedStatementsofCashFlows</Role>
      <ShortName>Consolidated Statements of Cash Flows</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>8</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R9.htm</HtmlFileName>
      <LongName>9952158 - Disclosure - Organization and Business Operations</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/OrganizationandBusinessOperations</Role>
      <ShortName>Organization and Business Operations</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>9</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R10.htm</HtmlFileName>
      <LongName>9952159 - Disclosure - Summary of Significant Accounting Policies</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SummaryofSignificantAccountingPolicies</Role>
      <ShortName>Summary of Significant Accounting Policies</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>10</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R11.htm</HtmlFileName>
      <LongName>9952160 - Disclosure - Accounting Changes and Error Corrections</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AccountingChangesandErrorCorrections</Role>
      <ShortName>Accounting Changes and Error Corrections</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>11</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R12.htm</HtmlFileName>
      <LongName>9952161 - Disclosure - Discontinued Operations</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DiscontinuedOperations</Role>
      <ShortName>Discontinued Operations</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>12</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R13.htm</HtmlFileName>
      <LongName>9952162 - Disclosure - Acquisition of Businesses</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AcquisitionofBusinesses</Role>
      <ShortName>Acquisition of Businesses</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>13</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R14.htm</HtmlFileName>
      <LongName>9952163 - Disclosure - Revenue</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/Revenue</Role>
      <ShortName>Revenue</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>14</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R15.htm</HtmlFileName>
      <LongName>9952164 - Disclosure - Operating Segment Data</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/OperatingSegmentData</Role>
      <ShortName>Operating Segment Data</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>15</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R16.htm</HtmlFileName>
      <LongName>9952165 - Disclosure - Inventory, Property, Plant and Equipment</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/InventoryPropertyPlantandEquipment</Role>
      <ShortName>Inventory, Property, Plant and Equipment</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>16</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R17.htm</HtmlFileName>
      <LongName>9952166 - Disclosure - Goodwill and Other Intangible Assets</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/GoodwillandOtherIntangibleAssets</Role>
      <ShortName>Goodwill and Other Intangible Assets</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>17</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R18.htm</HtmlFileName>
      <LongName>9952167 - Disclosure - Debt</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/Debt</Role>
      <ShortName>Debt</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>18</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R19.htm</HtmlFileName>
      <LongName>9952169 - Disclosure - Defined Benefit Plan</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DefinedBenefitPlan</Role>
      <ShortName>Defined Benefit Plan</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>19</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R20.htm</HtmlFileName>
      <LongName>9952170 - Disclosure - Stockholder's Equity</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/StockholdersEquity</Role>
      <ShortName>Stockholder's Equity</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>20</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R21.htm</HtmlFileName>
      <LongName>9952171 - Disclosure - Income Taxes</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/IncomeTaxes</Role>
      <ShortName>Income Taxes</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>21</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R22.htm</HtmlFileName>
      <LongName>9952172 - Disclosure - Fair Value Measurement</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/FairValueMeasurement</Role>
      <ShortName>Fair Value Measurement</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>22</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R23.htm</HtmlFileName>
      <LongName>9952173 - Disclosure - Noncontrolling Interest</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/NoncontrollingInterest</Role>
      <ShortName>Noncontrolling Interest</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>23</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R24.htm</HtmlFileName>
      <LongName>9952174 - Disclosure - Supplemental Data</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SupplementalData</Role>
      <ShortName>Supplemental Data</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>24</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R25.htm</HtmlFileName>
      <LongName>9952176 - Disclosure - Commitments and Contingencies</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/CommitmentsandContingencies</Role>
      <ShortName>Commitments and Contingencies</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>25</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R26.htm</HtmlFileName>
      <LongName>9952177 - Disclosure - Related Party Transactions</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/RelatedPartyTransactions</Role>
      <ShortName>Related Party Transactions</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>26</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R27.htm</HtmlFileName>
      <LongName>9952178 - Disclosure - Unaudited Quarterly Financial Data</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/UnauditedQuarterlyFinancialData</Role>
      <ShortName>Unaudited Quarterly Financial Data</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>27</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R28.htm</HtmlFileName>
      <LongName>9952179 - Disclosure - Valuation and Qualifying Accounts</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/ValuationandQualifyingAccounts</Role>
      <ShortName>Valuation and Qualifying Accounts</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>28</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R29.htm</HtmlFileName>
      <LongName>9952180 - Disclosure - Unaudited Quarterly Financial Data</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/UnauditedQuarterlyFinancialData_1</Role>
      <ShortName>Unaudited Quarterly Financial Data</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>29</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R30.htm</HtmlFileName>
      <LongName>9952181 - Disclosure - Subsequent Events</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SubsequentEvents</Role>
      <ShortName>Subsequent Events</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>30</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R31.htm</HtmlFileName>
      <LongName>995410 - Disclosure - Pay vs Performance Disclosure</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://xbrl.sec.gov/ecd/role/PvpDisclosure</Role>
      <ShortName>Pay vs Performance Disclosure</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>31</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R32.htm</HtmlFileName>
      <LongName>995445 - Disclosure - Insider Trading Arrangements</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://xbrl.sec.gov/ecd/role/InsiderTradingArrangements</Role>
      <ShortName>Insider Trading Arrangements</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>32</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R33.htm</HtmlFileName>
      <LongName>995447 - Disclosure - Insider Trading Policies and Procedures</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://xbrl.sec.gov/ecd/role/InsiderTradingPoliciesProc</Role>
      <ShortName>Insider Trading Policies and Procedures</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>33</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R34.htm</HtmlFileName>
      <LongName>9955511 - Disclosure - Summary of Significant Accounting Policies (Policies)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SummaryofSignificantAccountingPoliciesPolicies</Role>
      <ShortName>Summary of Significant Accounting Policies (Policies)</ShortName>
      <MenuCategory>Policies</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/SummaryofSignificantAccountingPolicies</ParentRole>
      <Position>34</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R35.htm</HtmlFileName>
      <LongName>9955512 - Disclosure - Revenue from Contract with Customer (Policies)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/RevenuefromContractwithCustomerPolicies</Role>
      <ShortName>Revenue from Contract with Customer (Policies)</ShortName>
      <MenuCategory>Policies</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/SummaryofSignificantAccountingPolicies</ParentRole>
      <Position>35</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R36.htm</HtmlFileName>
      <LongName>9955513 - Disclosure - Summary of Significant Accounting Policies (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SummaryofSignificantAccountingPoliciesTables</Role>
      <ShortName>Summary of Significant Accounting Policies (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/SummaryofSignificantAccountingPolicies</ParentRole>
      <Position>36</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R37.htm</HtmlFileName>
      <LongName>9955514 - Disclosure - Accounting Changes and Error Corrections (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AccountingChangesandErrorCorrectionsTables</Role>
      <ShortName>Accounting Changes and Error Corrections (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/AccountingChangesandErrorCorrections</ParentRole>
      <Position>37</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R38.htm</HtmlFileName>
      <LongName>9955515 - Disclosure - Discontinued Operations (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DiscontinuedOperationsTables</Role>
      <ShortName>Discontinued Operations (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/DiscontinuedOperations</ParentRole>
      <Position>38</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R39.htm</HtmlFileName>
      <LongName>9955517 - Disclosure - Revenue (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/RevenueTables</Role>
      <ShortName>Revenue (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/Revenue</ParentRole>
      <Position>39</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R40.htm</HtmlFileName>
      <LongName>9955518 - Disclosure - Operating Segment Data (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/OperatingSegmentDataTables</Role>
      <ShortName>Operating Segment Data (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/OperatingSegmentData</ParentRole>
      <Position>40</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R41.htm</HtmlFileName>
      <LongName>9955519 - Disclosure - Inventory, Property, Plant and Equipment (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/InventoryPropertyPlantandEquipmentTables</Role>
      <ShortName>Inventory, Property, Plant and Equipment (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/InventoryPropertyPlantandEquipment</ParentRole>
      <Position>41</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R42.htm</HtmlFileName>
      <LongName>9955520 - Disclosure - Goodwill and Other Intangible Assets (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/GoodwillandOtherIntangibleAssetsTables</Role>
      <ShortName>Goodwill and Other Intangible Assets (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/GoodwillandOtherIntangibleAssets</ParentRole>
      <Position>42</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R43.htm</HtmlFileName>
      <LongName>9955521 - Disclosure - Debt (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DebtTables</Role>
      <ShortName>Debt (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/Debt</ParentRole>
      <Position>43</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R44.htm</HtmlFileName>
      <LongName>9955522 - Disclosure - Defined Benefit Plan (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DefinedBenefitPlanTables</Role>
      <ShortName>Defined Benefit Plan (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/DefinedBenefitPlan</ParentRole>
      <Position>44</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R45.htm</HtmlFileName>
      <LongName>9955523 - Disclosure - Stockholder's Equity Stockholder's Equity (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/StockholdersEquityStockholdersEquityTables</Role>
      <ShortName>Stockholder's Equity Stockholder's Equity (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <Position>45</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R46.htm</HtmlFileName>
      <LongName>9955524 - Disclosure - Income Taxes (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/IncomeTaxesTables</Role>
      <ShortName>Income Taxes (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/IncomeTaxes</ParentRole>
      <Position>46</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R47.htm</HtmlFileName>
      <LongName>9955525 - Disclosure - Fair Value Measurement (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/FairValueMeasurementTables</Role>
      <ShortName>Fair Value Measurement (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/FairValueMeasurement</ParentRole>
      <Position>47</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R48.htm</HtmlFileName>
      <LongName>9955526 - Disclosure - Noncontrolling Interest (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/NoncontrollingInterestTables</Role>
      <ShortName>Noncontrolling Interest (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/NoncontrollingInterest</ParentRole>
      <Position>48</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R49.htm</HtmlFileName>
      <LongName>9955527 - Disclosure - Supplemental Data (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SupplementalDataTables</Role>
      <ShortName>Supplemental Data (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/SupplementalData</ParentRole>
      <Position>49</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R50.htm</HtmlFileName>
      <LongName>9955529 - Disclosure - Commitments and Contingencies (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/CommitmentsandContingenciesTables</Role>
      <ShortName>Commitments and Contingencies (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/CommitmentsandContingencies</ParentRole>
      <Position>50</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R51.htm</HtmlFileName>
      <LongName>9955530 - Disclosure - Related Party Transactions (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/RelatedPartyTransactionsTables</Role>
      <ShortName>Related Party Transactions (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/RelatedPartyTransactions</ParentRole>
      <Position>51</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R52.htm</HtmlFileName>
      <LongName>9955531 - Disclosure - Unaudited Quarterly Financial Data (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/UnauditedQuarterlyFinancialDataTables</Role>
      <ShortName>Unaudited Quarterly Financial Data (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/UnauditedQuarterlyFinancialData</ParentRole>
      <Position>52</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R53.htm</HtmlFileName>
      <LongName>9955532 - Disclosure - Summary of Significant Accounting Policies - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SummaryofSignificantAccountingPoliciesAdditionalInformationDetail</Role>
      <ShortName>Summary of Significant Accounting Policies - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>53</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R54.htm</HtmlFileName>
      <LongName>9955533 - Disclosure - Summary of Significant Accounting Policies - Summary of Ranges of Useful Lives (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SummaryofSignificantAccountingPoliciesSummaryofRangesofUsefulLivesDetail</Role>
      <ShortName>Summary of Significant Accounting Policies - Summary of Ranges of Useful Lives (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>54</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R55.htm</HtmlFileName>
      <LongName>9955534 - Disclosure - Accounting Changes and Error Corrections - Balance Sheet (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AccountingChangesandErrorCorrectionsBalanceSheetDetails</Role>
      <ShortName>Accounting Changes and Error Corrections - Balance Sheet (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>55</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R56.htm</HtmlFileName>
      <LongName>9955535 - Disclosure - Accounting Changes and Error Corrections - Balance Sheet - (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AccountingChangesandErrorCorrectionsBalanceSheetDetails_1</Role>
      <ShortName>Accounting Changes and Error Corrections - Balance Sheet - (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>56</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R57.htm</HtmlFileName>
      <LongName>9955536 - Disclosure - Accounting Changes and Error Corrections - Statement of Operations (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AccountingChangesandErrorCorrectionsStatementofOperationsDetails</Role>
      <ShortName>Accounting Changes and Error Corrections - Statement of Operations (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>57</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R58.htm</HtmlFileName>
      <LongName>9955537 - Disclosure - Accounting Changes and Error Corrections - Cash Flow (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AccountingChangesandErrorCorrectionsCashFlowDetails</Role>
      <ShortName>Accounting Changes and Error Corrections - Cash Flow (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>58</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R59.htm</HtmlFileName>
      <LongName>9955538 - Disclosure - Accounting Changes and Error Corrections - Restatement of Purchase Consideration (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AccountingChangesandErrorCorrectionsRestatementofPurchaseConsiderationDetails</Role>
      <ShortName>Accounting Changes and Error Corrections - Restatement of Purchase Consideration (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>59</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R60.htm</HtmlFileName>
      <LongName>9955539 - Disclosure - Discontinued Operations - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DiscontinuedOperationsAdditionalInformationDetail</Role>
      <ShortName>Discontinued Operations - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>60</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R61.htm</HtmlFileName>
      <LongName>9955540 - Disclosure - Discontinued Operations - Summary of Disposition of Operating Results (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DiscontinuedOperationsSummaryofDispositionofOperatingResultsDetail</Role>
      <ShortName>Discontinued Operations - Summary of Disposition of Operating Results (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>61</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R62.htm</HtmlFileName>
      <LongName>9955541 - Disclosure - Discontinued Operations - Summarized Balance Sheet Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DiscontinuedOperationsSummarizedBalanceSheetInformationDetails</Role>
      <ShortName>Discontinued Operations - Summarized Balance Sheet Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>62</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R63.htm</HtmlFileName>
      <LongName>9955542 - Disclosure - Acquisition of Businesses - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AcquisitionofBusinessesAdditionalInformationDetail</Role>
      <ShortName>Acquisition of Businesses - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>63</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R64.htm</HtmlFileName>
      <LongName>9955543 - Disclosure - Acquisition of Businesses Acquisition - Schedule of Assets Acquired and Liabilities Assumed as of the Acquisition Date (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AcquisitionofBusinessesAcquisitionScheduleofAssetsAcquiredandLiabilitiesAssumedasoftheAcquisitionDateDetails</Role>
      <ShortName>Acquisition of Businesses Acquisition - Schedule of Assets Acquired and Liabilities Assumed as of the Acquisition Date (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>64</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R65.htm</HtmlFileName>
      <LongName>9955544 - Disclosure - Acquisition of Businesses Acquisition - Schedule of Intangible Assets Recorded as Part of Acquisition (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AcquisitionofBusinessesAcquisitionScheduleofIntangibleAssetsRecordedasPartofAcquisitionDetails</Role>
      <ShortName>Acquisition of Businesses Acquisition - Schedule of Intangible Assets Recorded as Part of Acquisition (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>65</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R66.htm</HtmlFileName>
      <LongName>9955545 - Disclosure - Acquisition of Businesses Acquisition - Pro Forma Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/AcquisitionofBusinessesAcquisitionProFormaInformationDetails</Role>
      <ShortName>Acquisition of Businesses Acquisition - Pro Forma Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>66</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R67.htm</HtmlFileName>
      <LongName>9955546 - Disclosure - Revenue - Disaggregation of Revenue (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/RevenueDisaggregationofRevenueDetails</Role>
      <ShortName>Revenue - Disaggregation of Revenue (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>67</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R68.htm</HtmlFileName>
      <LongName>9955547 - Disclosure - Operating Segment Data - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/OperatingSegmentDataAdditionalInformationDetail</Role>
      <ShortName>Operating Segment Data - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>68</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R69.htm</HtmlFileName>
      <LongName>9955548 - Disclosure - Operating Segment Data - Summary of Net Sales of Operating Segments (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/OperatingSegmentDataSummaryofNetSalesofOperatingSegmentsDetail</Role>
      <ShortName>Operating Segment Data - Summary of Net Sales of Operating Segments (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>69</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R70.htm</HtmlFileName>
      <LongName>9955550 - Disclosure - Operating Segment Data - Summary of Profit (Loss) of Operating Segments (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/OperatingSegmentDataSummaryofProfitLossofOperatingSegmentsDetail</Role>
      <ShortName>Operating Segment Data - Summary of Profit (Loss) of Operating Segments (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>70</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R71.htm</HtmlFileName>
      <LongName>9955551 - Disclosure - Operating Segment Data - Summary of Accounts Receivable of Operating Segment (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/OperatingSegmentDataSummaryofAccountsReceivableofOperatingSegmentDetail</Role>
      <ShortName>Operating Segment Data - Summary of Accounts Receivable of Operating Segment (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>71</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R72.htm</HtmlFileName>
      <LongName>9955552 - Disclosure - Operating Segment Data - Summary of Goodwill and Identifiable Assets of Operating Segments (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/OperatingSegmentDataSummaryofGoodwillandIdentifiableAssetsofOperatingSegmentsDetail</Role>
      <ShortName>Operating Segment Data - Summary of Goodwill and Identifiable Assets of Operating Segments (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>72</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R73.htm</HtmlFileName>
      <LongName>9955553 - Disclosure - Operating Segment Data Operating Segment Data - Accounts Receivable and Identifiable Assets (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/OperatingSegmentDataOperatingSegmentDataAccountsReceivableandIdentifiableAssetsDetails</Role>
      <ShortName>Operating Segment Data Operating Segment Data - Accounts Receivable and Identifiable Assets (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>73</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R74.htm</HtmlFileName>
      <LongName>9955554 - Disclosure - Operating Segment Data Summary of Depreciation and Amortization Expense (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/OperatingSegmentDataSummaryofDepreciationandAmortizationExpenseDetails</Role>
      <ShortName>Operating Segment Data Summary of Depreciation and Amortization Expense (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>74</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R75.htm</HtmlFileName>
      <LongName>9955555 - Disclosure - Inventory, Property, Plant and Equipment - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/InventoryPropertyPlantandEquipmentAdditionalInformationDetail</Role>
      <ShortName>Inventory, Property, Plant and Equipment - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>75</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R76.htm</HtmlFileName>
      <LongName>9955556 - Disclosure - Inventory, Property, Plant and Equipment- Summary of Property, Plant and Equipment (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/InventoryPropertyPlantandEquipmentSummaryofPropertyPlantandEquipmentDetail</Role>
      <ShortName>Inventory, Property, Plant and Equipment- Summary of Property, Plant and Equipment (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>76</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R77.htm</HtmlFileName>
      <LongName>9955557 - Disclosure - Inventory, Property, Plant and Equipment - Summary of Inventory (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/InventoryPropertyPlantandEquipmentSummaryofInventoryDetail</Role>
      <ShortName>Inventory, Property, Plant and Equipment - Summary of Inventory (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>77</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R78.htm</HtmlFileName>
      <LongName>9955558 - Disclosure - Goodwill and Other Intangible Assets - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/GoodwillandOtherIntangibleAssetsAdditionalInformationDetail</Role>
      <ShortName>Goodwill and Other Intangible Assets - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>78</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R79.htm</HtmlFileName>
      <LongName>9955559 - Disclosure - Goodwill and Other Intangible Assets - Summary of Reconciliation of Change in Carrying Value of Goodwill (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/GoodwillandOtherIntangibleAssetsSummaryofReconciliationofChangeinCarryingValueofGoodwillDetail</Role>
      <ShortName>Goodwill and Other Intangible Assets - Summary of Reconciliation of Change in Carrying Value of Goodwill (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>79</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R80.htm</HtmlFileName>
      <LongName>9955560 - Disclosure - Goodwill and Other Intangible Assets - Summary of Other Intangible Assets (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/GoodwillandOtherIntangibleAssetsSummaryofOtherIntangibleAssetsDetail</Role>
      <ShortName>Goodwill and Other Intangible Assets - Summary of Other Intangible Assets (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>80</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R81.htm</HtmlFileName>
      <LongName>9955561 - Disclosure - Goodwill and Other Intangible Assets - Summary of Estimated Charges to Amortization Expense of Intangible Assets (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/GoodwillandOtherIntangibleAssetsSummaryofEstimatedChargestoAmortizationExpenseofIntangibleAssetsDetail</Role>
      <ShortName>Goodwill and Other Intangible Assets - Summary of Estimated Charges to Amortization Expense of Intangible Assets (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>81</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R82.htm</HtmlFileName>
      <LongName>9955562 - Disclosure - Goodwill and Other Intangible Asset - Carrying Amount of Goodwill (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/GoodwillandOtherIntangibleAssetCarryingAmountofGoodwillDetails</Role>
      <ShortName>Goodwill and Other Intangible Asset - Carrying Amount of Goodwill (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>82</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R83.htm</HtmlFileName>
      <LongName>9955563 - Disclosure - Goodwill and Other Intangible Assets Goodwill and Other Intangible Asset - Carrying Amount of Goodwill Reconciliation By Segment (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/GoodwillandOtherIntangibleAssetsGoodwillandOtherIntangibleAssetCarryingAmountofGoodwillReconciliationBySegmentDetails</Role>
      <ShortName>Goodwill and Other Intangible Assets Goodwill and Other Intangible Asset - Carrying Amount of Goodwill Reconciliation By Segment (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>83</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R84.htm</HtmlFileName>
      <LongName>9955564 - Disclosure - Debt - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DebtAdditionalInformationDetail</Role>
      <ShortName>Debt - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>84</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R85.htm</HtmlFileName>
      <LongName>9955565 - Disclosure - Debt - Summary of Debt Holdings (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DebtSummaryofDebtHoldingsDetail</Role>
      <ShortName>Debt - Summary of Debt Holdings (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>85</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R86.htm</HtmlFileName>
      <LongName>9955566 - Disclosure - Debt - Summary of Annual Maturities of Term Loan Facility and Revolving Credit Facility (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DebtSummaryofAnnualMaturitiesofTermLoanFacilityandRevolvingCreditFacilityDetail</Role>
      <ShortName>Debt - Summary of Annual Maturities of Term Loan Facility and Revolving Credit Facility (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>86</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R87.htm</HtmlFileName>
      <LongName>9955567 - Disclosure - Debt - Issuance Costs (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DebtIssuanceCostsDetails</Role>
      <ShortName>Debt - Issuance Costs (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>87</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R88.htm</HtmlFileName>
      <LongName>9955568 - Disclosure - Debt - Summary of Actual Financial Ratios as Part of Affirmative Covenants Credit Facility (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DebtSummaryofActualFinancialRatiosasPartofAffirmativeCovenantsCreditFacilityDetail</Role>
      <ShortName>Debt - Summary of Actual Financial Ratios as Part of Affirmative Covenants Credit Facility (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>88</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R89.htm</HtmlFileName>
      <LongName>9955569 - Disclosure - Debt - Summary of Components of Interest Expense (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DebtSummaryofComponentsofInterestExpenseDetail</Role>
      <ShortName>Debt - Summary of Components of Interest Expense (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>89</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R90.htm</HtmlFileName>
      <LongName>9955570 - Disclosure - Derivative Instruments and Hedging Activities - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DerivativeInstrumentsandHedgingActivitiesAdditionalInformationDetail</Role>
      <ShortName>Derivative Instruments and Hedging Activities - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>90</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R91.htm</HtmlFileName>
      <LongName>9955571 - Disclosure - Defined Benefit Plan - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DefinedBenefitPlanAdditionalInformationDetail</Role>
      <ShortName>Defined Benefit Plan - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>91</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R92.htm</HtmlFileName>
      <LongName>9955573 - Disclosure - Defined Benefit Plan - Summary of Net Periodic Benefit Cost (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DefinedBenefitPlanSummaryofNetPeriodicBenefitCostDetail</Role>
      <ShortName>Defined Benefit Plan - Summary of Net Periodic Benefit Cost (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>92</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R93.htm</HtmlFileName>
      <LongName>9955574 - Disclosure - Defined Benefit Plan - Summary of Assumptions Used to Determine the Benefit Obligations and Components of the Net Periodic Benefit Cost (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DefinedBenefitPlanSummaryofAssumptionsUsedtoDeterminetheBenefitObligationsandComponentsoftheNetPeriodicBenefitCostDetail</Role>
      <ShortName>Defined Benefit Plan - Summary of Assumptions Used to Determine the Benefit Obligations and Components of the Net Periodic Benefit Cost (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>93</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R94.htm</HtmlFileName>
      <LongName>9955575 - Disclosure - Defined Benefit Plan - Summary of Expected Foreign Plan Benefit Payments (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DefinedBenefitPlanSummaryofExpectedForeignPlanBenefitPaymentsDetail</Role>
      <ShortName>Defined Benefit Plan - Summary of Expected Foreign Plan Benefit Payments (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>94</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R95.htm</HtmlFileName>
      <LongName>9955576 - Disclosure - Defined Benefit Plan - Summary of Allocation of Assets in Swiss Life's Group Life Portfolio (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/DefinedBenefitPlanSummaryofAllocationofAssetsinSwissLifesGroupLifePortfolioDetail</Role>
      <ShortName>Defined Benefit Plan - Summary of Allocation of Assets in Swiss Life's Group Life Portfolio (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>95</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R96.htm</HtmlFileName>
      <LongName>9955577 - Disclosure - Stockholder's Equity - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/StockholdersEquityAdditionalInformationDetail</Role>
      <ShortName>Stockholder's Equity - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>96</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R97.htm</HtmlFileName>
      <LongName>9955578 - Disclosure - Stockholder's Equity Stockholders' Equity - Summary of Basic and Diluted Earnings Per Share (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/StockholdersEquityStockholdersEquitySummaryofBasicandDilutedEarningsPerShareDetails</Role>
      <ShortName>Stockholder's Equity Stockholders' Equity - Summary of Basic and Diluted Earnings Per Share (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>97</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R98.htm</HtmlFileName>
      <LongName>9955579 - Disclosure - Income Taxes - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/IncomeTaxesAdditionalInformationDetail</Role>
      <ShortName>Income Taxes - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>98</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R99.htm</HtmlFileName>
      <LongName>9955580 - Disclosure - Income Taxes - Components of the Company's pretax income (loss) before taxes (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/IncomeTaxesComponentsoftheCompanyspretaxincomelossbeforetaxesDetails</Role>
      <ShortName>Income Taxes - Components of the Company's pretax income (loss) before taxes (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>99</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R100.htm</HtmlFileName>
      <LongName>9955581 - Disclosure - Income Taxes - Components of the Company's Income Tax Provision (Benefit) (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/IncomeTaxesComponentsoftheCompanysIncomeTaxProvisionBenefitDetail</Role>
      <ShortName>Income Taxes - Components of the Company's Income Tax Provision (Benefit) (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>100</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R101.htm</HtmlFileName>
      <LongName>9955582 - Disclosure - Income Taxes - Summary of Deferred Tax Assets and Deferred Tax Liabilities (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/IncomeTaxesSummaryofDeferredTaxAssetsandDeferredTaxLiabilitiesDetail</Role>
      <ShortName>Income Taxes - Summary of Deferred Tax Assets and Deferred Tax Liabilities (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>101</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R102.htm</HtmlFileName>
      <LongName>9955583 - Disclosure - Income Taxes - Reconciliation Between Federal Statutory Rate and Effective Income Tax Rate (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/IncomeTaxesReconciliationBetweenFederalStatutoryRateandEffectiveIncomeTaxRateDetail</Role>
      <ShortName>Income Taxes - Reconciliation Between Federal Statutory Rate and Effective Income Tax Rate (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>102</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R103.htm</HtmlFileName>
      <LongName>9955584 - Disclosure - Income Taxes - Reconciliation of Unrecognized Tax Benefits (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/IncomeTaxesReconciliationofUnrecognizedTaxBenefitsDetail</Role>
      <ShortName>Income Taxes - Reconciliation of Unrecognized Tax Benefits (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>103</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R104.htm</HtmlFileName>
      <LongName>9955585 - Disclosure - Fair Value Measurement - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/FairValueMeasurementAdditionalInformationDetail</Role>
      <ShortName>Fair Value Measurement - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>104</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R105.htm</HtmlFileName>
      <LongName>9955586 - Disclosure - Fair Value Measurement - Summary of Assets and Liabilities Carried at Fair Value Measured on Recurring Basis (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/FairValueMeasurementSummaryofAssetsandLiabilitiesCarriedatFairValueMeasuredonRecurringBasisDetail</Role>
      <ShortName>Fair Value Measurement - Summary of Assets and Liabilities Carried at Fair Value Measured on Recurring Basis (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>105</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R106.htm</HtmlFileName>
      <LongName>9955587 - Disclosure - Fair Value Measurement - Reconciliations of Change in Carrying Value of Level 3 Supplemental Put Liability (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/FairValueMeasurementReconciliationsofChangeinCarryingValueofLevel3SupplementalPutLiabilityDetail</Role>
      <ShortName>Fair Value Measurement - Reconciliations of Change in Carrying Value of Level 3 Supplemental Put Liability (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>106</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R107.htm</HtmlFileName>
      <LongName>9955588 - Disclosure - Fair Value Measurement - Summary of Assets and Liabilities Carried at Fair Value Measured on Non-recurring Basis (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/FairValueMeasurementSummaryofAssetsandLiabilitiesCarriedatFairValueMeasuredonNonrecurringBasisDetail</Role>
      <ShortName>Fair Value Measurement - Summary of Assets and Liabilities Carried at Fair Value Measured on Non-recurring Basis (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>107</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R108.htm</HtmlFileName>
      <LongName>9955589 - Disclosure - Noncontrolling Interest - Company's Ownership Percentage of its Majority Owned Operating Segments and Related Noncontrolling Interest (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/NoncontrollingInterestCompanysOwnershipPercentageofitsMajorityOwnedOperatingSegmentsandRelatedNoncontrollingInterestDetail</Role>
      <ShortName>Noncontrolling Interest - Company's Ownership Percentage of its Majority Owned Operating Segments and Related Noncontrolling Interest (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>108</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R109.htm</HtmlFileName>
      <LongName>9955590 - Disclosure - Noncontrolling Interest - Summary of Each Purchase of Noncontrolling Interest (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/NoncontrollingInterestSummaryofEachPurchaseofNoncontrollingInterestDetail</Role>
      <ShortName>Noncontrolling Interest - Summary of Each Purchase of Noncontrolling Interest (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>109</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R110.htm</HtmlFileName>
      <LongName>9955591 - Disclosure - Supplemental Data - Summary of Supplemental Balance Sheet Data (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SupplementalDataSummaryofSupplementalBalanceSheetDataDetail</Role>
      <ShortName>Supplemental Data - Summary of Supplemental Balance Sheet Data (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>110</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R111.htm</HtmlFileName>
      <LongName>9955592 - Disclosure - Supplemental Data - Summary of Supplemental Cash Flow Data (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SupplementalDataSummaryofSupplementalCashFlowDataDetail</Role>
      <ShortName>Supplemental Data - Summary of Supplemental Cash Flow Data (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>111</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R112.htm</HtmlFileName>
      <LongName>9955593 - Disclosure - Supplemental Data - Statement of Operations (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SupplementalDataStatementofOperationsDetails</Role>
      <ShortName>Supplemental Data - Statement of Operations (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>112</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R113.htm</HtmlFileName>
      <LongName>9955594 - Disclosure - Equity Method Investment - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/EquityMethodInvestmentAdditionalInformationDetail</Role>
      <ShortName>Equity Method Investment - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>113</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R114.htm</HtmlFileName>
      <LongName>9955595 - Disclosure - Commitments and Contingencies - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/CommitmentsandContingenciesAdditionalInformationDetail</Role>
      <ShortName>Commitments and Contingencies - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>114</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R115.htm</HtmlFileName>
      <LongName>9955596 - Disclosure - Commitments and Contingencies - Summary of Future Minimum Rental Commitments under Operating Leases (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/CommitmentsandContingenciesSummaryofFutureMinimumRentalCommitmentsunderOperatingLeasesDetail</Role>
      <ShortName>Commitments and Contingencies - Summary of Future Minimum Rental Commitments under Operating Leases (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>115</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R116.htm</HtmlFileName>
      <LongName>9955597 - Disclosure - Related Party Transactions - Additional Information (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/RelatedPartyTransactionsAdditionalInformationDetail</Role>
      <ShortName>Related Party Transactions - Additional Information (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>116</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R117.htm</HtmlFileName>
      <LongName>9955598 - Disclosure - Related Party Transactions - Schedule of Incurred Management Fees (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/RelatedPartyTransactionsScheduleofIncurredManagementFeesDetail</Role>
      <ShortName>Related Party Transactions - Schedule of Incurred Management Fees (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>117</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R118.htm</HtmlFileName>
      <LongName>9955599 - Disclosure - Unaudited Quarterly Financial Data - Summary of Unaudited Quarterly Financial Data (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/UnauditedQuarterlyFinancialDataSummaryofUnauditedQuarterlyFinancialDataDetail</Role>
      <ShortName>Unaudited Quarterly Financial Data - Summary of Unaudited Quarterly Financial Data (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>118</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R119.htm</HtmlFileName>
      <LongName>9955600 - Disclosure - Schedule II - Valuation and Qualifying Accounts (Detail)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/ScheduleIIValuationandQualifyingAccountsDetail</Role>
      <ShortName>Schedule II - Valuation and Qualifying Accounts (Detail)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>119</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R120.htm</HtmlFileName>
      <LongName>9955601 - Disclosure - Unaudited Quarterly Financial Data - Consolidated Balance Sheets (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/UnauditedQuarterlyFinancialDataConsolidatedBalanceSheetsDetails</Role>
      <ShortName>Unaudited Quarterly Financial Data - Consolidated Balance Sheets (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>120</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R121.htm</HtmlFileName>
      <LongName>9955602 - Disclosure - Unaudited Quarterly Financial Data - Consolidated Balance Sheets - (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/UnauditedQuarterlyFinancialDataConsolidatedBalanceSheetsDetails_1</Role>
      <ShortName>Unaudited Quarterly Financial Data - Consolidated Balance Sheets - (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>121</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R122.htm</HtmlFileName>
      <LongName>9955603 - Disclosure - Unaudited Quarterly Financial Data - Consolidated Statements of Operations (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/UnauditedQuarterlyFinancialDataConsolidatedStatementsofOperationsDetails</Role>
      <ShortName>Unaudited Quarterly Financial Data - Consolidated Statements of Operations (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>122</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R123.htm</HtmlFileName>
      <LongName>9955604 - Disclosure - Unaudited Quarterly Financial Data - Consolidated Statements of Cash Flows (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/UnauditedQuarterlyFinancialDataConsolidatedStatementsofCashFlowsDetails</Role>
      <ShortName>Unaudited Quarterly Financial Data - Consolidated Statements of Cash Flows (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>123</Position>
    </Report>
    <Report instance="codi-20241231.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R124.htm</HtmlFileName>
      <LongName>9955605 - Disclosure - Subsequent Events (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.compasstrust.com/role/SubsequentEventsDetails</Role>
      <ShortName>Subsequent Events (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.compasstrust.com/role/SubsequentEvents</ParentRole>
      <Position>124</Position>
    </Report>
    <Report>
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <LongName>All Reports</LongName>
      <ReportType>Book</ReportType>
      <ShortName>All Reports</ShortName>
    </Report>
  </MyReports>
  <InputFiles>
    <File doctype="10-K/A" isDefinitelyFs="true" isUsgaap="true" original="codi-20241231.htm">codi-20241231.htm</File>
    <File>codi-20241231.xsd</File>
    <File>codi-20241231_cal.xml</File>
    <File>codi-20241231_def.xml</File>
    <File>codi-20241231_lab.xml</File>
    <File>codi-20241231_pre.xml</File>
  </InputFiles>
  <SupplementalFiles>
    <File>codi-20241231_g1.jpg</File>
    <File>codi-20241231_g2.jpg</File>
  </SupplementalFiles>
  <BaseTaxonomies>
    <BaseTaxonomy items="3">http://fasb.org/srt/2024</BaseTaxonomy>
    <BaseTaxonomy items="6785">http://fasb.org/us-gaap/2024</BaseTaxonomy>
    <BaseTaxonomy items="50">http://xbrl.sec.gov/dei/2024</BaseTaxonomy>
    <BaseTaxonomy items="5">http://xbrl.sec.gov/ecd/2024</BaseTaxonomy>
  </BaseTaxonomies>
  <HasPresentationLinkbase>true</HasPresentationLinkbase>
  <HasCalculationLinkbase>true</HasCalculationLinkbase>
</FilingSummary>
