You will want a separate team build definition per branch there, and they may all use the same build process template that does the workflow you describe. I think there is some confusion here as you are not really interested in building a solution that is open on a developer's machine, but rather what is stored in version control (your real "version of the truth").
I think we are headed down the wrong path to worry about what solution is open on a devs machine, etc.
I think we are headed down the wrong path to worry about what solution is open on a devs machine, etc.