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 subdomain.domain1.org and typing in that URL gets you to a page where you see a a theme and branding specific to domain1.org. Site2 would be domain2.org and likewise going to that site you would see a theme and branding specific to domain2.org, 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 subdomain.domain1.org/domain2 and subdomain.domain1.org/domain3. Then use the Domain Mapping plugin to map domain2.org to subdomain.domain1.org/domain2 and domain3.org to subdomain.domain2.org/domain3.

Then I would want to continue to be able to make new users like domain2.org/names and domain3.org/names.

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