A build agent can connect to only one specific TeamCity server right?
Why this restriction? If the TeamCity server versions are the same, it should be no problem having a build agent serving many TeamCity servers, provided that it is ensured that only one build can run at the same time on that agent.
I have TeamCity on a productive system and on a test system (because I do REST calls against TeamCity and first want to test that on a isolated system), but want to reuse the productive agents because of simplicity.
Just an idea.