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

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-06-05</periodOfReport>

    <issuer>
        <issuerCik>0001643615</issuerCik>
        <issuerName>Onterris, Inc.</issuerName>
        <issuerTradingSymbol>ONT</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001053442</rptOwnerCik>
            <rptOwnerName>GRAHAM PETER</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>5120 NORTHSHORE DR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NORTH LITTLE ROCK</rptOwnerCity>
            <rptOwnerState>AR</rptOwnerState>
            <rptOwnerZipCode>72118</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>true</isDirector>
            <isOfficer>false</isOfficer>
            <isTenPercentOwner>false</isTenPercentOwner>
            <isOther>false</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>false</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2026-06-05</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>false</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>25140</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.19</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>256689</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price. These shares of common stock of the Issuer were purchased in multiple transactions by the Reporting Person at prices ranging from $17.00 to $17.46, inclusive. The Reporting Person undertakes to provide upon request by the Commission staff, the Issuer, or a security holder of the Issuer full information regarding the number of shares of common stock acquired at each separate price within the range.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Nasym Afsari, Attorney in Fact</signatureName>
        <signatureDate>2026-06-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
