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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-06-06</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001655265</rptOwnerCik>
            <rptOwnerName>MDP Global Investors II Ltd</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MAPLES AND CALDER</rptOwnerStreet1>
            <rptOwnerStreet2>PO BOX 309, UGLAND HOUSE</rptOwnerStreet2>
            <rptOwnerCity>GRAND CAYMAN</rptOwnerCity>
            <rptOwnerState>E9</rptOwnerState>
            <rptOwnerZipCode>KYI-1104</rptOwnerZipCode>
            <rptOwnerStateDescription>CAYMAN ISLANDS</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001601029</rptOwnerCik>
            <rptOwnerName>Mustang Investment Holdings L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O MAPLES AND CALDER</rptOwnerStreet1>
            <rptOwnerStreet2>PO BOX 309, UGLAND HOUSE</rptOwnerStreet2>
            <rptOwnerCity>GRAND CAYMAN</rptOwnerCity>
            <rptOwnerState>E9</rptOwnerState>
            <rptOwnerZipCode>KY1-1104</rptOwnerZipCode>
            <rptOwnerStateDescription>CAYMAN ISLANDS</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>2017-06-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>23482216</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Mustang Investment Holdings L.P.</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Disposed of in exchange for $18.00 per share pursuant to the Agreement and Plan of Merger, dated as of January 23, 2017, by and among the Issuer, WestRock Company and WRK Merger Sub Limited (&quot;Merger Sub&quot;), pursuant to which Merger Sub was merged with and into the Issuer, with the Issuer surviving such merger.</footnote>
        <footnote id="F2">The reported shares were held by Mustang Investment Holdings L.P. (&quot;Mustang Holdings&quot;).  MDP Global Investors II Limited (&quot;MDP Limited&quot;) is the general partner of Mustang Holdings and as a result may be deemed to share beneficial ownership of the reported shares.  MDP Limited hereby disclaims beneficial ownership of the shares held by Mustang Holdings, except to the extent of its pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>MDP Global Investors II Limited, By: /s/ Annie S. Terry, Principal, Deputy General Counsel and Chief Compliance Officer</signatureName>
        <signatureDate>2017-06-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Mustang Investment Holdings L.P., By: MDP Global Investors II Limited, its general partner, By: /s/ Annie S. Terry, Principal, Deputy General Counsel and Chief Compliance Officer</signatureName>
        <signatureDate>2017-06-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
