Team City 9.1 Rest API: How to run build with custom config setting (settings from VCS / not current ones) through Rest API

Question

I am trying to run a personal build on a specified change through Rest API. If I ran the build though "Run Custom Build" dialog in UI, there is an option to specify which changes to include and which project config settings to use but I couldn't find a way to specify custom config settings through Rest API.

<build>
  <triggeringOptions cleanSources="true" rebuildAllDependencies="true"/>
  <buildType id="buildConfID"/>
  <lastChanges>
    <change id="modificationId"/>
  </lastChanges>
</build>