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

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:01a08cad-472d-7a80-a95c-09ed073b7eef,g:4149dc94-6470-46c8-acfc-b8d737da8b69-->
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:nsp="http://www.insperity.com/20261029" attributeFormDefault="unqualified" elementFormDefault="qualified" targetNamespace="http://www.insperity.com/20261029">
  <xs:import namespace="http://fasb.org/us-gaap/2026" schemaLocation="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd"/>
  <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/2026" schemaLocation="https://xbrl.sec.gov/dei/2026/dei-2026.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="nsp-20261029_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="nsp-20261029_def.xml" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef" 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="nsp-20261029_lab.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:type="simple"/>
      <link:roleType id="DocumentandEntityInformationDocument" roleURI="http://www.insperity.com/role/DocumentandEntityInformationDocument">
        <link:definition>0000001 - Document - Document and Entity Information 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>
