Persephone's Pick Your Poison was a very interesting and unusual format. Essentially there was an approved list of match-ups (in this case, a lopsided list and an even list). Players took turns picking which MU they wanted, and then their opponent picked which side of it they would play. So each person picked two lopsided MUs where their opponent would decide to play the side they felt was most advantaged, and then you both picked one even MU, and then one player picked a last even MU which would be the Ace Match, if the set went that long.
There are team events as well, though those can be trickier to organize. I think they all had 'team' in the name somewhere. This would be either full cast standard CP, or would involve a draft of characters first.
Yomi draft and reverse draft is another way of building a stable of characters to play.
For events that use stables "losing character is eliminated" leads to the loser of the 1st match receiving a disadvantage, compared to "winning character is eliminated." For that reason I think 'stable' tournaments have tended to move to the Conquest fomat (winning character can no longer be picked).
Persephone's Pick Your Poison involved drafting MUs, rather than individual characters.
Some of the events that Zqxx has put on had extremely limited casts - only Rook and BBB, for example.
There have been a couple of double-blind events. Instead of switching to standard CP after the results of the first match, both players pick from their legal list of characters in double-blind fashion again after each match is complete. There are pros and cons to this approach. Mathematically, it should lead to less lopsided match-ups being selected, I think? LK4O4 wrote a ton of material about this that went over my head on the old forums. However, you can have situations where players pick into a bad match-up again and again, which is a deal-breaker for some.
One format that Sirlin explained to me at FSX this year was interesting and may be worth a look, but I can't remember the exact details. It's essentially a 'stable' format (you pick three characters from the cast, and you can only play characters from that limited pool during the event), but instead of being double-blind into standard CP, each match both players randomly roll for their character. Each game involves randomly re-rolling from within each player's stable, but there was some additional rule about characters being locked out that I can't remember. It may have been, like, each pair of characters that just played are frozen out for one game, or something? I feel like it was more involved than that...
The stated advantages of the format are that it makes counterpicking largely ineffective, because you will now random roll into lopsided games occasionally, rather than the winner of a match almost always being put into their worst MU in standard CP format. There was an argument that this would then also reduce the degree to which Troq/Geiger/Zane would be picked, since they are often picked as CPs. I'm not sure I would agree with that 2nd argument, but it would still be an interesting format to try.
The difficulty of the format, especially played in the Steam client, is that you don't have a way to randomly roll for characters in a fair way. So there would need to be a TO involved in each match (or ahead of time in the scheduling conversation) for this format to work.
@Sirlin would you mind outlining the format rules?