Multi-domains, Mult-brand, Single domain

I would like to have 3 BP networks with three separate brands and three separate URLs, but them all using the same database. That is, a user signed up in site3 can see, group with, friend, email, etc a user in site 1 seamlessly.

So site1 would be and typing in that URL gets you to a page where you see a a theme and branding specific to Site2 would be and likewise going to that site you would see a theme and branding specific to, and likewise for site3.

The independent branding is important, but the ability to have cross site networking is important as well.

On solution I thought of is the following:

Set up BP network with users and Then use the Domain Mapping plugin to map to and to

Then I would want to continue to be able to make new users like and

Or is this all possible using the Multi-domains plugin?