The 320 is almost the same boat and is my current favorite. But there are plenty of 34's out there too.
It's NOT "almost the same boat." By far.
I had lunch the other day with a friend who used to have a 320 and now has a 34. He says they are completely different boats. The freeboard is much higher on the 320. The rig is different. He said the 320 rounds up more than his 34 because of the beamier sections aft on the 320, and as well the 320 rudder tends to loose its bite when heeled going upwind. This is what he said, and he's had BOTH boats; I've never sailed a 320 although I've had my 34 for 18 years now and have sailed it up the coast from California to Vancouver Island. We both felt that the layout down below ended up getting it backwards (compared to the spacious C34), because when you sit on the settee you end up looking at the wall of the head, and not the relatively open space of the galley. Same footprint (almost) but vastly different visual perceptions. Think about it now that you know, and compare the layouts when you go on board each boat. I think Beneteau got their 35 foot boats all wrong because of this same layout issue from the three Beneteaus of that size range I've chartered.
You HAVE TO determine how you intend to use the boat you choose. Given what I knew before I spoke with my friend and what I knew before that, it's simply a reality of different horses for courses.
That said, the C320 is another solid boat from Catalina.
But you're looking for a larger boat from Catalina than the one you have. There's more than the 320 or 34 to choose from. But you knew that, right?