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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-03-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001590714</issuerCik>
        <issuerName>Platform Specialty Products Corp</issuerName>
        <issuerTradingSymbol>PAH</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001336528</rptOwnerCik>
            <rptOwnerName>Pershing Square Capital Management, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>888 SEVENTH AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>42ND FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001336477</rptOwnerCik>
            <rptOwnerName>PS Management GP, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>888 SEVENTH AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>42ND FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001056513</rptOwnerCik>
            <rptOwnerName>ACKMAN WILLIAM A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>888 SEVENTH AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>42ND FLOOR</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10019</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2014-03-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>X</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4166665</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.50</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>33333330</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Warrants to purchase Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>11.50</value>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2014-03-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>X</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>12500001</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2013-05-22</value>
            </exerciseDate>
            <expirationDate>
                <value>2016-10-31</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>0.333</value>
                    <footnoteId id="F5"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">In addition to Pershing Square Capital Management, L.P., a Delaware limited partnership (&quot;Pershing Square Capital&quot;), this Form 4 is being filed jointly by PS Management GP, LLC, a Delaware limited liability company (&quot;PS Management&quot;), and William A. Ackman, a citizen of the United States of America (collectively, the &quot;Reporting Persons&quot;), each of whom has the same business address as Pershing Square Capital and may be deemed to have a pecuniary interest in securities reported by it on this Form 4 (the &quot;Subject Securities&quot;).</footnote>
        <footnote id="F2">Pershing Square Capital advises the accounts of Pershing Square, L.P., a Delaware limited partnership (&quot;PS&quot;), Pershing Square II, L.P., a Delaware limited partnership (&quot;PS II&quot;), Pershing Square International, Ltd., a Cayman Islands exempted company (together with its wholly-owned subsidiary PSRH, Inc., a Cayman Islands exempted company, &quot;PS International&quot;), and Pershing Square Holdings, Ltd., a limited liability company incorporated in Guernsey (&quot;PSH&quot; and together with PS, PS II and PS International, the &quot;Pershing Square Funds&quot;).</footnote>
        <footnote id="F3">Pershing Square Capital, as the investment adviser to the Pershing Square Funds, may be deemed to be the beneficial owner of the Subject Securities for purposes of Rule 16a-1(a) of the Securities Exchange Act of 1934. As the general partner of Pershing Square Capital, PS Management may be deemed to be the beneficial owner of the Subject Securities for purposes of Rule 16a-1(a). By virtue of William A. Ackman's position as Chief Executive Officer of Pershing Square Capital and managing member of PS Management, William A. Ackman may be deemed to be the beneficial owner of the Subject Securities for purposes of Rule 16a-1(a).</footnote>
        <footnote id="F4">Each of the Reporting Persons disclaims any beneficial ownership of any of the Subject Securities, except to the extent of any pecuniary interest therein.</footnote>
        <footnote id="F5">12,500,001 warrants. Each three (3) warrants entitles the holder on exercise to buy one (1) share of Common Stock for $11.50.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>PERSHING SQUARE CAPITAL MANAGEMENT, L.P., By: PS Management GP, LLC, its General Partner By: /s/ William A. Ackman, William A. Ackman, Managing Member</signatureName>
        <signatureDate>2014-03-11</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>PS MANAGEMENT GP, LLC, By: /s/ William A. Ackman, Managing Member</signatureName>
        <signatureDate>2014-03-11</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ William A. Ackman, Managing Member</signatureName>
        <signatureDate>2014-03-11</signatureDate>
    </ownerSignature>
</ownershipDocument>
