<?xml version="1.0" encoding="US-ASCII"?>
<!-- Generated by Broadridge Transform (tm) - http://www.broadridge.com -->
<!-- Created: Wed Apr 29 12:08:29 UTC 2026 -->
<xs:schema elementFormDefault="qualified" targetNamespace="http://compasstherapeutics.com/20260610" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:us-types="http://xbrl.us/us-types/2009-01-31" xmlns:cmpx="http://compasstherapeutics.com/20260610" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" xmlns:dtr="http://www.xbrl.org/dtr/type/2024-01-31" xmlns:xbrli="http://www.xbrl.org/2003/instance">
  <xs:annotation>
    <xs:appinfo>
      <link:linkbaseRef xlink:type="simple" xlink:href="cmpx-20260610_lab.xml" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef"/>
      <link:linkbaseRef xlink:type="simple" xlink:href="cmpx-20260610_pre.xml" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef"/>
      <link:linkbaseRef xlink:type="simple" xlink:href="cmpx-20260610_def.xml" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef"/>
    </xs:appinfo>
  </xs:annotation>
  <xs:import namespace="http://www.xbrl.org/2003/instance" schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/2003/linkbase" schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/ecd/2025" schemaLocation="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/dei/2025" schemaLocation="https://xbrl.sec.gov/dei/2025/dei-2025.xsd"/>
  <xs:import namespace="http://www.xbrl.org/2009/role/negated" schemaLocation="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd"/>
  <xs:import namespace="http://www.xbrl.org/dtr/type/2024-01-31" schemaLocation="https://www.xbrl.org/dtr/type/2024-01-31/types.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/ecd-sub/2025" schemaLocation="https://xbrl.sec.gov/ecd/2025/ecd-sub-2025.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/dei-sub/2025" schemaLocation="https://xbrl.sec.gov/dei/2025/dei-sub-2025.xsd"/>
  <xs:import namespace="http://xbrl.org/2005/xbrldt" schemaLocation="http://www.xbrl.org/2005/xbrldt-2005.xsd"/>
  <xs:element name="ThomasSchuetzMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="cmpx_ThomasSchuetzMember"/>
<!-- [WMV7][xgWjmRKqTP+Do6AAcFyMKFPJD6ScUOSE1xJV15uAMUpOa6X6bxqhwTjNNeGH97vnIwLjEBemoIx6x0qs8mhES9N2HqcvGD47IKK0BPEs36ok+ev8jxEgJkHAtlfAW8xIuvgD/8bWy2r4y+8dUXA/GWbAmTYtwPmm5/Il+I+yrhF9oS+QayMVJZ+NLoYsz9RTa0RdZYfBv9cg4IfwFfpq2ZJyyX/8TMMp7Euvy1kMXWTXCxYldyNuFGV+W7hdcwr4yUW1xa8/FqzefAa3NyhcgGcPVRFyidq5ODmIiT+NmSlfHQNnsOdJPsBI3RJAcK28glonbXHp1LeH/MYz9rt05PMs+qlpxslAN+N/sm6frReFLaWCotR8DXgeEsp5nZoz8Q==] CSR-->
  <xs:element name="VeredBiskerLeibMember" type="dtr:domainItemType" abstract="true" xbrli:periodType="duration" nillable="true" substitutionGroup="xbrli:item" id="cmpx_VeredBiskerLeibMember"/>
</xs:schema>
