You can technically make your own Trinity Limit, as I mentioned that it will differ depending on who triggers it. And for those who have them, they have to pick two specific people; obviously we're only just starting to get people coming in with their CSs, so they have them open ended. That doesn't mean that just because they have their own that they can't be in other people's, however.

Example would be:

Sora, Riku, and Kairi make up Trinity Limit A which belongs to Sora. Riku is missing and is replaced with Roxas, so Sora cannot execute his Trinity Limit A. However, Kairi has Trinity Limit B, which consists of herself, Roxas and Sora, so she is able to execute it. Meanwhile Roxas has Trinity Limit C with himself, Axel and Sora--Axel is not around, so he cannot use his Trinity Limit. Even if Sora doesn't have the required people for HIS Trinity Limit, if he is part of ANOTHER Trinity Limit, then whoever owns it (Which in this case would be Kairi, as her Trinity Limit has everyone present) is able to use it as long as they have the needed party members.

That should clear things up (I hope so).