I discuss this at https://grantkillian.wordpress.com/2018/12/17/how-i-add-custom-sitecore-publishing-service-targets/. Essentially, there are 3 main locations to update the sc.publishing.xml file to support additional publishing targets. This sample illustrates the 3 (under Publishing/ConnectionStrings, under Services/DefaultConnectionFactory/Op…

ReferenceSample.sc.publishing.xml

<?xml version="1.0" encoding="UTF-8"?>
<Settings>
   <Sitecore>
      <Publishing>
         <InstanceName>${SITECORE_InstanceName}</InstanceName>
         <ConnectionStrings>
            <Service>${Sitecore:Publishing:ConnectionStrings:Master}</Service>
            <!-- Add any additional publishing targets you may use (first location for changes to this file) -->
            <previewweb>Data Source=Server-012345;Initial Catalog=PrevWeb;Integrated Security=True;MultipleActiveResultSets=True;ConnectRetryCount=15;ConnectRetryInterval=1</previewweb>
            <liveweb>Data Source=Server-012345;Initial Catalog=LiveWeb;Integrated Security=True;MultipleActiveResultSets=True;ConnectRetryCount=15;ConnectRetryInterval=1</liveweb>
            <!-- end first location for changes -->
         </ConnectionStrings>
         <Services>
            <DefaultConnectionFactory>
               <Options>
                  <Connections>
                     <Links>
                        <Type>Sitecore.Framework.Publishing.Data.AdoNet.SqlDatabaseConnection, Sitecore.Framework.Publishing.Data</Type>
                        <LifeTime>Transient</LifeTime>
                        <Options>
                           <ConnectionString>${Sitecore:Publishing:ConnectionStrings:Core}</ConnectionString>
                           <DefaultCommandTimeout>120</DefaultCommandTimeout>
                           <Behaviours>
                              <backend>sql-backend-default</backend>
                              <api>sql-api-default</api>
                           </Behaviours>
                        </Options>
                     </Links>
                     <Service>
                        <Type>Sitecore.Framework.Publishing.Data.AdoNet.SqlDatabaseConnection, Sitecore.Framework.Publishing.Data</Type>
                        <LifeTime>Transient</LifeTime>
                        <Options>
                           <ConnectionString>${Sitecore:Publishing:ConnectionStrings:Service}</ConnectionString>
                           <DefaultCommandTimeout>120</DefaultCommandTimeout>
                           <Behaviours>
                              <backend>sql-backend-default</backend>
                              <api>sql-api-default</api>
                           </Behaviours>
                        </Options>
                     </Service>
                     <Master>
                        <Type>Sitecore.Framework.Publishing.Data.AdoNet.SqlDatabaseConnection, Sitecore.Framework.Publishing.Data</Type>
                        <LifeTime>Transient</LifeTime>
                        <Options>
                           <ConnectionString>${Sitecore:Publishing:ConnectionStrings:Master}</ConnectionString>
                           <DefaultCommandTimeout>120</DefaultCommandTimeout>
                           <Behaviours>
                              <backend>sql-backend-default</backend>
                              <api>sql-api-default</api>
                           </Behaviours>
                        </Options>
                     </Master>
                     <Internet>
                        <!-- Should match the name of the publishing target configured in SC. -->
                        <Type>Sitecore.Framework.Publishing.Data.AdoNet.SqlDatabaseConnection, Sitecore.Framework.Publishing.Data</Type>
                        <LifeTime>Transient</LifeTime>
                        <Options>
                           <ConnectionString>${Sitecore:Publishing:ConnectionStrings:Web}</ConnectionString>
                           <DefaultCommandTimeout>120</DefaultCommandTimeout>
                           <Behaviours>
                              <backend>sql-backend-default</backend>
                              <api>sql-api-default</api>
                           </Behaviours>
                        </Options>
                     </Internet>
                     <!-- start custom publishing target additions  (2nd location) -->
                     <Preview>
                        <!-- Should match the name of the publishing target configured in Sitecore -->
                        <Type>Sitecore.Framework.Publishing.Data.AdoNet.SqlDatabaseConnection, Sitecore.Framework.Publishing.Data</Type>
                        <LifeTime>Transient</LifeTime>
                        <Options>
                           <ConnectionString>${Sitecore:Publishing:ConnectionStrings:previewweb}</ConnectionString>
                           <DefaultCommandTimeout>120</DefaultCommandTimeout>
                           <Behaviours>
                              <backend>sql-backend-default</backend>
                              <api>sql-api-default</api>
                           </Behaviours>
                        </Options>
                     </Preview>
                     <Live>
                        <!-- Should match the name of the publishing target configured in Sitecore -->
                        <Type>Sitecore.Framework.Publishing.Data.AdoNet.SqlDatabaseConnection, Sitecore.Framework.Publishing.Data</Type>
                        <LifeTime>Transient</LifeTime>
                        <Options>
                           <ConnectionString>${Sitecore:Publishing:ConnectionStrings:liveweb}</ConnectionString>
                           <DefaultCommandTimeout>120</DefaultCommandTimeout>
                           <Behaviours>
                              <backend>sql-backend-default</backend>
                              <api>sql-api-default</api>
                           </Behaviours>
                        </Options>
                     </Live>
                     <!-- end custom publishing target additions (2nd location) -->
                  </Connections>
               </Options>
            </DefaultConnectionFactory>
            <DbConnectionBehaviours>
               <Options>
                  <Entries>
                     <sql-backend-default>
                        <Type>Sitecore.Framework.Publishing.Data.AdoNet.NoRetryConnectionBehaviour, Sitecore.Framework.Publishing.Data</Type>
                        <Options>
                           <Name>Default Backend No Retry behaviour</Name>
                           <CommandTimeout>120</CommandTimeout>
                        </Options>
                     </sql-backend-default>
                     <sql-api-default>
                        <Type>Sitecore.Framework.Publishing.Data.AdoNet.NoRetryConnectionBehaviour, Sitecore.Framework.Publishing.Data</Type>
                        <Options>
                           <Name>Default Api No Retry behaviour</Name>
                           <CommandTimeout>10</CommandTimeout>
                        </Options>
                     </sql-api-default>
                  </Entries>
               </Options>
            </DbConnectionBehaviours>
            <StoreFactory>
               <Options>
                  <Stores>
                     <Service>
                        <Type>Sitecore.Framework.Publishing.Data.ServiceStore, Sitecore.Framework.Publishing.Data</Type>
                        <ConnectionName>Service</ConnectionName>
                        <FeaturesListName>ServiceStoreFeatures</FeaturesListName>
                     </Service>
                     <Sources>
                        <Master>
                           <Type>Sitecore.Framework.Publishing.Data.SourceStore, Sitecore.Framework.Publishing.Data</Type>
                           <ConnectionNames>
                              <master>Master</master>
                           </ConnectionNames>
                           <FeaturesListName>SourceStoreFeatures</FeaturesListName>
                           <!-- The name of the Database entity in Sitecore. -->
                           <ScDatabase>master</ScDatabase>
                        </Master>
                     </Sources>
                     <Targets>
                        <!--Additional targets can be configured here-->
                        <Internet>
                           <Type>Sitecore.Framework.Publishing.Data.TargetStore, Sitecore.Framework.Publishing.Data</Type>
                           <ConnectionName>Internet</ConnectionName>
                           <FeaturesListName>TargetStoreFeatures</FeaturesListName>
                           <!-- The id of the target item definition in Sitecore. -->
                           <Id>8E080626-DDC3-4EF4-A1D1-F0BE4A200254</Id>
                           <!-- The name of the Database entity in Sitecore. -->
                           <ScDatabase>web</ScDatabase>
                        </Internet>
                        <!-- start custom publishing target additions (third location) -->
                        <!-- this XML node should be named the same as the item in Sitecore (not the "Display Name", but the Item name) -->
                        <Preview>
                           <Type>Sitecore.Framework.Publishing.Data.TargetStore, Sitecore.Framework.Publishing.Data</Type>
                           <ConnectionName>Preview</ConnectionName>
                           <FeaturesListName>TargetStoreFeatures</FeaturesListName>
                           <!-- make sure the GUID below matches the GUID stored in Sitecore for the Publishing Target -->
                           <Id>8D1249E6-9413-4C2D-8C72-06561CE1D026</Id>
                           <ScDatabase>preveiwweb</ScDatabase>
                        </Preview>
                        <!-- this XML node should be named the same as the item in Sitecore (not the "Display Name", but the Item name) -->
                        <Live>
                           <Type>Sitecore.Framework.Publishing.Data.TargetStore, Sitecore.Framework.Publishing.Data</Type>
                           <ConnectionName>Live</ConnectionName>
                           <FeaturesListName>TargetStoreFeatures</FeaturesListName>
                           <!-- make sure the GUID below matches the GUID stored in Sitecore for the Publishing Target -->
                           <Id>0EA57D57-7837-4B51-A72C-E8B3F1322C07</Id>
                           <ScDatabase>liveweb</ScDatabase>
                        </Live>
                        <!-- end custom publishing target additions (third location)  -->
                     </Targets>
                     <ItemsRelationship>
                        <Type>Sitecore.Framework.Publishing.Data.ItemsRelationshipStore, Sitecore.Framework.Publishing.Data</Type>
                        <ConnectionName>Links</ConnectionName>
                        <FeaturesListName>ItemsRelationshipStoreFeatures</FeaturesListName>
                     </ItemsRelationship>
                  </Stores>
               </Options>
            </StoreFactory>
            <StoreFeaturesLists>
               <Options>
                  <FeatureLists>
                     <!--Source Store Features-->
                     <SourceStoreFeatures>
                        <ItemReadRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.Data.CompositeItemReadRepository, Sitecore.Framework.Publishing.Data</Type>
                        </ItemReadRepositoryFeature>
                        <TestableContentRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.Data.CompositeTestableContentRepository, Sitecore.Framework.Publishing.Data</Type>
                        </TestableContentRepositoryFeature>
                        <WorkflowStateRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.Data.CompositeWorkflowStateRepository, Sitecore.Framework.Publishing.Data</Type>
                        </WorkflowStateRepositoryFeature>
                        <EventQueueRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.Data.CompositeEventQueueRepository, Sitecore.Framework.Publishing.Data</Type>
                           <options>
                              <ConnectionName>master</ConnectionName>
                           </options>
                        </EventQueueRepositoryFeature>
                        <SourceIndexFeature>
                           <Type>Sitecore.Framework.Publishing.ItemIndex.SourceIndexWrapper, Sitecore.Framework.Publishing</Type>
                        </SourceIndexFeature>
                     </SourceStoreFeatures>
                     <!--Service Store Features-->
                     <ServiceStoreFeatures>
                        <ManifestRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.Manifest.ManifestRepository, Sitecore.Framework.Publishing</Type>
                        </ManifestRepositoryFeature>
                        <PublisherOperationRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.PublisherOperations.PublisherOperationRepository, Sitecore.Framework.Publishing</Type>
                        </PublisherOperationRepositoryFeature>
                        <PublishJobQueueRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.PublishJobQueue.PublishJobQueueRepository, Sitecore.Framework.Publishing</Type>
                        </PublishJobQueueRepositoryFeature>
                        <TargetSyncStateRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.TargetSyncState.TargetSyncStateRepository, Sitecore.Framework.Publishing</Type>
                        </TargetSyncStateRepositoryFeature>
                        <ActivationLockRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.InstanceActivation.ActivationLockRepository, Sitecore.Framework.Publishing</Type>
                        </ActivationLockRepositoryFeature>
                     </ServiceStoreFeatures>
                     <!--Target Store Features-->
                     <TargetStoreFeatures>
                        <IndexableItemRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.Data.Classic.ClassicIndexableItemRepository, Sitecore.Framework.Publishing.Data.Classic</Type>
                        </IndexableItemRepositoryFeature>
                        <ItemWriteRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.Data.Classic.ClassicItemRepository, Sitecore.Framework.Publishing.Data.Classic</Type>
                        </ItemWriteRepositoryFeature>
                        <MediaRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.Data.Classic.Repositories.ClassicMediaRepository, Sitecore.Framework.Publishing.Data.Classic</Type>
                        </MediaRepositoryFeature>
                        <TargetIndexFeature>
                           <Type>Sitecore.Framework.Publishing.ItemIndex.TargetIndexWrapper, Sitecore.Framework.Publishing</Type>
                        </TargetIndexFeature>
                     </TargetStoreFeatures>
                     <!--ItemsRelationship Store Features-->
                     <ItemsRelationshipStoreFeatures>
                        <DatabaseItemRelationshipRepositoryFeature>
                           <Type>Sitecore.Framework.Publishing.Data.Classic.ClassicItemRelationshipRepository, Sitecore.Framework.Publishing.Data.Classic</Type>
                        </DatabaseItemRelationshipRepositoryFeature>
                     </ItemsRelationshipStoreFeatures>
                  </FeatureLists>
               </Options>
            </StoreFeaturesLists>
         </Services>
      </Publishing>
   </Sitecore>
</Settings>