One build engine for two projects?

I have an original project with one stream, four build definitions and one build engine which builds all four build definitions successfully.

I have created a new project in the same repo, with new streams, teams and build definitions. I would like to use the existing build engine process to run the new builds, and while its definition shows the new definition in the list of supported build definitions, the build requests remain in 'pending' state.

A build engine seems to belong to a particular team area (this one is still in the original team area), could that be the problem? Are build engines intended to support build definitions across multiple projects and/or streams/teams?

Thanks, Alex.