BuddyPress Group "Types"

So I'm working on a project that has very specific needs, and after trying various ways to go about it, I'm still not sure I'm doing anything right.

What I essentially need is multiple group components, with similar functionality, but no overlap in terms of search, loops etc. This can be compared perhaps to CPT's each with their own archive.

Is this possible, and how can I go about getting that?

To illustrate in more depth:
I'd like one "Chapters" group type, and another "Projects" group type. The "projects" a user belongs to doesn't add to his "chapters" count and vice versa.