Multisite BuddyPress


Having posted in a few different places I'm still confused as to whether this is even possible, could anyone shed any light on this please...?

I have a WP multisite install that looks like this:

There are is a common theme across all the sites on the multisite, and also common plugins.

What I would like is BP activated for each site, such that each site has its own set of users, its own feeds, in effect a 'BPMU'

Users of site1 for example only see user activity that is associated with site1.

Is this even possible?