shri I think Franz has already answered your question in part. Instead of allowing users to create their own sub-forums, as Dakoom suggested, you'd simply be creating them yourself. So it seems that part would be easy enough.
But having data beyond logins shared globally strikes me as another matter. Like you, I don't know enough about the architecture to say for sure, but my rather badly educated guess is: it would be possible but not quite as easy.
Not much of an answer, I know. But I was wondering if you'd considered the possibility of using Flarum's tagging system to achieve your ends. Since you can assign more than one tag to any given thread, you could assign one set of tags to identify the locations that can be applied to each thread (these could be the ones that show up on the Tags page), and another set for your categories or topics. It might even be possible to create a plugin that would constrain tag behavior, so users would be required to assign at least one (but not more than one) of the location tags to each thread. Then just make "global" another location. I think this sort of arrangement could allow you to obtain your objectives with a single installation.
I have a hunch this sort of plugin might be easier to do than the other sort...