I've never really paid much attention to Pazaak in all the times I've played through KotOR2. I played a couple of rounds with Atton and with people in the cantina on Nar Shaddaa, but that was about it.

 

However, I've seen people discuss other rule-sets and talk about players other than the Exile and Atton playing Pazaak. So is there some progression by which if you play the game often enough, you're able to play Pazaak with other team-members/to slightly different rules? Because if so, it might just give me an excuse to run through the game again. I'd hate to be missing out on any fun!

No- same rules, just better cards in your side-deck. Atton's the only one who plays with you.

Matron