In April, CEO of Index, Atlus' parent company, Yoshimi Ogawa had said that "she hopes to develop a variety of content business opportunities for Catherine", labelling it Atlus' next new IP following in Megami Tensei's and Etrian Odyssey's footsteps.  
 
Continued development in the "Catherine" franchise could mean as little as Japan-only social games, but if there was to be an actual sequel, what would you want from it? Would you want returning characters, returning locations, more puzzles, less puzzles, a different puzzle mechanic...? 
 
Source

I would definitely want it fleshed out a little bit more.  And frankly, strip out the whole meter system.  Just give me a bunch of questions at the end if you must insist that there be multiple endings.  I wouldn't mind seeing the characters again, I liked the writing for Vincent and his buddies, but, I honestly can't think of a good way to bring them back.  And definitely a new puzzle mechanic if it was the returning characters would make the most sense, since Vincent has been basically promised he'll never have to do that again.
 
I think, most of all, I'd like to see the balance of story gameplay versus puzzle gameplay lean much more heavily on the story stuff.  My favorite part was wandering the Stray Sheep.
 
Really, though, I don't know that I want a sequel that's just a rehash of the same story... and I don't know how they'd do it otherwise.

Really, though, I don't know that I want a sequel that's just a rehash of the same story... and I don't know how they'd do it otherwise.

Keep golden playhouse but make it several shorter twighlight zone like episodes.

I don't think I would want a sequel to Catherine, recurring characters or not. I can't see much that you can do with it in order to keep the story interesting and always have a twist. Though, I guess, if there had to be a sequel I would want to see more varied gameplay or at least a better core mechanic.

@kingzetta said:

Keep golden playhouse but make it several shorter twighlight zone like episodes.

That actually sounds pretty awesome.

@DonutFever said:

Wouldn't want the cast to be the exact same, though Boss, Trisha and Catherine would make sense. Game-wise, I would want more things to do during the Stray Sheep-equivalent of the game.

I would want it to have all the original cast in some major capacity. A new cheater as the main character could work though.

@kingzetta said:

Keep golden playhouse but make it several shorter twighlight zone like episodes.

Or this. That sounds like it could be great.

I don't want a Catherine sequel. I love the game, but a huge part is because is because the game is a huge breath of fresh air.
 
Don't waste the Persona team's time with another sequel laden franchise>:( more new IPs plz

If they were to make a sequel, I think there should be more non-puzzle gameplay segments instead of just the bar. I think Vincent and his gang have to return, because I grew really attached to those guys by the end of the game. Orlando especially, because he's a champ.