In my experience the thing to do is find a single protein you KNOW will work, and feed only that for at least a month.
Here's a quick rundown of my experience with Jitzu:
When I took over Jitzu's care she was 2yrs old, unspayed, and cranky/untrusting and generally awful. The girl who was 'looking after her' was feeding her whatever was cheapest at the grocery store. When she remembered to buy cat food. (I got quite a few pets when she moved out and 'couldn't take them with her'. *glowers* Some people should NOT be allowed to own pets!)
At that point, and for the next year or so (until I learned better) she continued to be fed grocery store food, although I bought what looked like the best stuff there. (Yeah, we all know how reliable labels can be, lol.) She was also throwing up as much as 3-4 times every day.
Once I wised up and started feeding her a higher quality kibble she did ok for a bit, only throwing up 1-2 times a day for the first 4 months. Then it went right back to awful. I asked a few vets, and they all said cats throwing up were 'normal' but I could try their special cat food if I wanted.
Long story short, we tried a LOT of vet foods, meds, and many other kinds of kibble - grain free included - before I did a bit more research (found CF
) and switched to all grain free wet. She did ok on that, but after about 4 months she was getting sick again.
A bit more research and I finally decided to give raw food a shot. Switched all 4 cats (since I'd accumulated Torri and the boys along the way) to raw. After 1 month on raw (we were doing a meal plan, chicken breasts/thighs mixed with this nutrient powder stuff) her personality improved a TON.
Jitzu went from being a gigantic PITA who growled and chased the other cats, guests, and even me, to actually being nice sometimes. I eve caught her playing and grooming Doran! HUGE difference. That's when I decided I'd never switch her back to processed foods.
Now, 6 years later, she's still got a picky tummy. She'll get sick if she licks plates left dirty in the sink, or if she steals food, or if I feed her the wrong things...but I'm way better at managing her diet and her attitude kept improving once she started feeling better.
The biggest thing I found with her is that she was still really reactive to new food up to 1 year after the switch. So, I started gently. We fed mostly chicken and pork for the first year (with me making their meals myself - frankenprey model raw), and after that gradually introducing other meats. Anything too fatty will set her off, so will eating too fast. But now she gets sick a max of once a week - usually because she's stolen something or eaten too fast.
I'd suggest picking one thing and really sticking to it. Long term that isn't manageable on raw, but with allergies priority 1 is to get their digestive tract soothed. When they've been constantly exposed to allergens it keeps their system on high alert, and that means more likely to reject foods that they aren't actually allergic to. Once the system is given time to calm down you may find you can feed a broader variety of raw meats. But you HAVE to give him time to calm his digestive tract first.