I think Denti way back on page 1 had it right. I think it would be P2 for the pilot who was not the designated commander.
Rudestuff. Different companies and national agencies rules may (will!) vary but I can see various scenarios where two captain could fly together. For example, I heard of a Royal Flight in the Middle East where all the pilots were both captains and all were right seat checked to ensure maximum flexibility. Alternatively a captain who needs landings for recency so the trainer occupies the right seat and acts as PM for both sectors. I’m sure there are other examples.
I think you’ve misread Rudestuff’s post, he’s not saying two pilots qualified as captains can’t fly together, he’s saying that when they do only one is the captain, the other is the FO, regardless of qualification.