I'd like to know what you're calling a "premium food." To the vast majority of people, and even to the vast majority of vets, things like Science Diet and Iams are premium.
No, they're not. In fact, Science Diet is pretty crappy. Iams used to be a bit better, but not since they did
major changes to their formula.
Expanding further on what froggy7 said, in case there's either a sensitivity or outright allergy, I would eliminate
all grains. And the seafood. I don't know where you are. In the U.S. we feed a lot of beef and seafood, and usually you want to eliminate those to check for allergies. Poultry seems to be OK. But you could also try just some of the odd things like duck, venison, rabbit. I hear in Europe they already feed a lot of things like duck & rabbit. So then the idea is eliminate those and maybe try just poultry or something. The idea is to get away from seafood and to get away from what has been fed a lot. Sometimes allergies are to things they get a lot of. (True of people too.)
Read the cans very carefully, as even when it says chicken & liver, it may still contain fish, unidentified "meat" by-products, or unidentified "liver" etc. And then you don't know what you're really getting. Truly premium foods state exactly what is in them. For instance, byNature Naturals pouched chicken & liver has chicken and chicken liver. The rest is supplements. No hiding fish or other unidentified stuff.
Here are some foods with no seafood or grains. This is assuming you don't buy a seafood flavor. By "no seafood" I mean no
hidden seafood. Active Life, Avoderm (select cuts), by Nature Naturals & Organics, Innova EVO
95% meat varieties (also a good choice for duck & venison), Nature's Variety
Instincts (they have lamb, venison, duck & rabbit). Yes, I know, limited list. There are probably some I haven't heard of (yet). Petsmart carries some. And some can be found in health food stores. These are the truly premium foods, which most people have never heard of.
If you try this and the problems stop, you can then start slowly adding certain things back in. (I would still avoid corn like the plague, and leave seafood to last.)
BTW, contrary to popular belief, cats don't need to be eating dry food, and in fact, shouldn't be. So don't even make that an issue that he can't eat it. I don't think I'm aware of ANY dry food that doesn't contain grains of some sort. They're mostly high carb, which cats don't process as well and can cause diabetes later in life. And they're dry, meaning lack of moisture, which can lead to urinary tract problems and even kidney disease later in life. Cats don't naturally drink a lot and they don't drink enough on dry to make up for the lack of moisture. And especially a cat who is puking and needs some extra moisture. You might try encouraging him to drink more, like with a water fountain, or even if he likes drinking from the running faucet. (I'd normally suggest a bit of tuna juice in the water, but not if you're checking for allergies.) And dry foods does
not help their teeth. Maybe theoretically, but not in practice. There's a ton of cats out there with major dental problems, disease, and teeth falling out who've been on dry food their whole lifes. Obviously it isn't doing anything. (They must chew the food and they really don't. Chewing bones would help.)
I'm assuming you've thought of things like hairballs. Like be sure to brush/comb him each day to get as much extra fur out.
Not sure what you mean by "sores" on his mouth, but here's page you might want to look at:
Feline Outreach - Education
And please, please, please try to avoid steroids!