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

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-10-14</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0002102123</issuerCik>
        <issuerName>Apogee Acquisition Corp</issuerName>
        <issuerTradingSymbol>AACP</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0002124513</rptOwnerCik>
            <rptOwnerName>Watson Thomas Lloyd</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>C/O APOGEE ACQUISITION CORP</rptOwnerStreet1>
            <rptOwnerStreet2>2106 HOUSE AVE SUITE 375</rptOwnerStreet2>
            <rptOwnerCity>CHEYENNE</rptOwnerCity>
            <rptOwnerState>WY</rptOwnerState>
            <rptOwnerZipCode>82001</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Operating Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Class B Ordinary Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2026-10-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>36000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Ordinary Shares</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>36000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>24000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents Class B ordinary shares which will automatically convert into Class A ordinary shares concurrently with or immediately following the consummation of the initial business combination of Apogee Acquisition Corp, or earlier at the option of the holder on a one-for-one basis, subject to adjustment, as described in the Registration Statement on Form S-1 (File No. 333-294102) related to the Issuer's initial public offering.</footnote>
        <footnote id="F2">Reflects the forfeiture of 36,000 Class B Ordinary Shares to Apogee Acquisition Sponsor LLC (the &quot;Sponsor&quot;) for no consideration, in connection with Mr. Watson's resignation from his role as Chief Operating Officer of the Issuer, pursuant to the terms of Mr. Watson's securities assignment and forfeiture agreement with the Sponsor.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Thomas Lloyd Watson</signatureName>
        <signatureDate>2026-10-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
