I'm using as a reference the 9.x api documentation at (https://confluence.jetbrains.com/display/TCD9/REST+API).
In there, I can find the right rest command to modify an existing project's parent project:
Project's parent project: GET/PUT XML
But!, according to what I can understand, it requires an xml payload and that payload is not documented (or I cannot find it :)).
Can someone help me out?