Multi-project multi-team Scrum

Question

2 teams (A and B) in different geo locations are developing Project P.

Both of the teams are also developing few other smaller projects: A has projects PA1 and PA2. B has PB1 and PB2. P is the only one common to the 2 teams.

The Scrum design today:

• Each team has a PO, and they decide on the priorities together.
• One common Backlog that contains stories from project P and from PA1 and PA2. PB1 and PB2 are done off-scrum.
• Each team has its own sprint and SM. Team A picks stories from the backlog that are related to projects P, PA1 and PA2. Team B takes stories only related to P.

The problem:

• I want to manage PB1 and PB2 in Scrum as well.

Possible solutions:

• Add PB1 and PB2 to the same Backlog? - will complicate the backlog even more than now.
• Separate to 3 backlogs (P, PA1-2, PB1-2)? - There is a rule of "one backlog per team"... Should we break it? And is it even supported in TFS?

Any idea how to solve the problem?