<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:019ce86d-a070-7a3b-86ca-e57586406f57,g:a0fcc3b1-5ce7-47ee-9d4e-d5d4329c20e5-->
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:intl="http://www.intlfcstone.com/20260312" attributeFormDefault="unqualified" elementFormDefault="qualified" targetNamespace="http://www.intlfcstone.com/20260312">
  <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/dei/2025" schemaLocation="https://xbrl.sec.gov/dei/2025/dei-2025.xsd"/>
  <xs:annotation>
    <xs:appinfo>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="intl-20260312_pre.xml" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="intl-20260312_lab.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:type="simple"/>
      <link:roleType id="CoverDocument" roleURI="http://www.intlfcstone.com/role/CoverDocument">
        <link:definition>0000001 - Document - Cover Document</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
    </xs:appinfo>
  </xs:annotation>
</xs:schema>
