When updating an Application's stage in an ATS, there are some processes that must be followed to get a 200 Ok or 201 Created!
Best Practice
Verify that the Application ID exists by doing a GET /Application request first.
If you would like to create the Application, you must do POST Application first.
Verify that the Job Interview Stage exists by doing a GET /job-interview-stages request.
Verify that the Job Interview Stage you would like to update the application to, is not already attached to that application.
You can do this by performing a GET /Applications request and seeing what stage the application is current at.
Verify that the remote user exists by doing a GET /users request.
Follow this body:
{"job_interview_stage":"2893420374902374","remote_user_id":"8234b3j248c87ns0s08s08f0sj"}
Please see the Field Support by Platform for that integration to see what else is required.