Can a server instance that has a db in one existing bdr group add that same db to a different/new bdr group so that the db belongs to two different bdr groups at the same time?
Not at the moment, and it's not planned or really designed.
Different DBs can be, but a given DB must be in only one BDR group.
The only way what you describe could work would be if the DB had non-overlapping schemas, i.e. no tables were shared between both. Not only that, but all data types, functions, etc that had the same names would have to have identical definitions.
I don't really see a compelling use case for doing this, and at this point I don't think anyone's thought hard about it.
What _is_ planned (and implemented, but barely tested and not officially supported) is to permit multiple UDR upstreams. So you can receive changesets from multiple upstream servers, which themselves might be BDR nodes.
I'd be interested in a description of your intended use case for what you describe. What problem would it solve for you?
