Net Income (Loss) Per Share Attributable to Class A Common Shareholders - Schedule of Calculations of Basic and Diluted Net Income (Loss) Per Share (Parenthetical) (Details) - shares	3 Months Ended	9 Months Ended
Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2025	Sep. 30, 2024
Class A Common Stock
Earnings Per Share Basic [Line Items]
Number of shares of common stock to be issued upon exchange of a partnership unit	1		1
Fully diluted shares of common stock outstanding if all Class A partnership units were to be exchanged for common stock immediately following the reorganization	86,203,342	82,966,406	85,505,786	82,269,323
Restricted Stock and RSUs
Earnings Per Share Basic [Line Items]
Number of antidilutive securities excluded from calculation of diluted income (loss) per share	0	887	357,110	3,856

Represents the number of shares to be issued upon exchange of each unit.

No definition available.

Name:	mc_NumberOfSharesIssuableUponExchangeOfEachUnit
Namespace Prefix:	mc_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Represents the number of shares issued and outstanding and to be used in calculating diluted EPS, if all partnership units of specified class were to be exchanged for common stock immediately following the reorganization.

+ References

No definition available.

+ Details

Name:	mc_WeightedAverageNumberOfShareOutstandingDilutedIfAllUnitsExchangedForCommonStockImmediatelyFollowingReorganization
Namespace Prefix:	mc_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Securities (including those issuable pursuant to contingent stock agreements) that could potentially dilute basic earnings per share (EPS) or earnings per unit (EPU) in the future that were not included in the computation of diluted EPS or EPU because to do so would increase EPS or EPU amounts or decrease loss per share or unit amounts for the period presented.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 260
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482662/260-10-50-1

+ Details

Name:	us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 260
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482662/260-10-50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 260
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482689/260-10-45-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 260
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482689/260-10-45-3

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 260
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 60B
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482689/260-10-45-60B

+ Details

Name:	us-gaap_EarningsPerShareBasicLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassAMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis=mc_RestrictedStockAndRestrictedStockUnitsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: