<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-10-21</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001645926</issuerCik>
        <issuerName>Multi Packaging Solutions International Ltd</issuerName>
        <issuerTradingSymbol>MPSX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001654048</rptOwnerCik>
            <rptOwnerName>Chesapeake Holdings Ltd.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE CARLYLE GROUP</rptOwnerStreet1>
            <rptOwnerStreet2>1001 PENNSYLVANIA AVE. NW, SUITE 220 S.</rptOwnerStreet2>
            <rptOwnerCity>WASHINGTON</rptOwnerCity>
            <rptOwnerState>DC</rptOwnerState>
            <rptOwnerZipCode>20004-2505</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001653976</rptOwnerCik>
            <rptOwnerName>Chase-Mustang Newco Ltd.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE CARLYLE GROUP</rptOwnerStreet1>
            <rptOwnerStreet2>1001 PENNSYLVANIA AVE. NW, SUITE 220 S.</rptOwnerStreet2>
            <rptOwnerCity>WASHINGTON</rptOwnerCity>
            <rptOwnerState>DC</rptOwnerState>
            <rptOwnerZipCode>20004-2505</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001653873</rptOwnerCik>
            <rptOwnerName>Chesapeake Finance 1 Ltd.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE CARLYLE GROUP</rptOwnerStreet1>
            <rptOwnerStreet2>1001 PENNSYLVANIA AVE. NW, SUITE 220 S.</rptOwnerStreet2>
            <rptOwnerCity>WASHINGTON</rptOwnerCity>
            <rptOwnerState>DC</rptOwnerState>
            <rptOwnerZipCode>20004-2505</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2015-10-21</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>30969716</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents a pro rata distribution in-kind of the shares formerly held by Chesapeake Finance 1 Ltd. to all shareholders of Chesapeake Holdings Ltd.</footnote>
        <footnote id="F2">Chesapeake Holdings Ltd. is the sole shareholder of Chase-Mustang Newco Ltd., which is the sole shareholder of Chesapeake Finance 1 Ltd.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Chesapeake Holdings Ltd. By: Zeina Bain Director</signatureName>
        <signatureDate>2015-10-23</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Chase-Mustang Newco Ltd. By:  Zeina Bain, Director</signatureName>
        <signatureDate>2015-10-23</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Chesapeake Finance 1 Ltd. By:  Zeina Bain, Director</signatureName>
        <signatureDate>2015-10-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
