I would like to configure a TeamCity pipeline that uses the concept of build promotion to integrate with outside tools. I have done something similar with Jenkins using the Promoted Builds Plugin. Basically you set up a number of promotions for the initial build/compile job that can be dependent on each other to form a heirarchy. As the build progresses and passes certain milestones, the build can be "promoted" which can trigger other jobs, etc. Through their REST API, you can query the most recent build at a certain promotion level and can trigger a "manual" promotion via the API as well.
How can I do the same thing in TeamCity? I don't see an API for promotion and it seems like the promotion lives on each "downstream" build configuration, not the initial build configuration. Or is there is a way to do this via some other mechanism without resorting to coding a plugin?