We suspected a food allergy in one of my cats. The course my vet recommended for this was to switch him to a special diet (containing no previously-eaten proteins) for a few months and then, if that made it better, re-introduce old proteins one at a time to see which he reacts to -- possibly with iterations.
My cat's allergy turned out not to be to food, but this got me wondering: many foods, both canned and dry, use a combination of ingredients, so he'd been exposed to all the biggies (chicken, turkey, beef, tuna, other seafood, etc) and possibly even to some of the less-common ones (lamb, duck, a stray mouse...). If I were trying to isolate a food allergy, I'd have to pick one of those at a time to try.
Can we improve on random choice? Is there any research on what are the most common food allergies in cats?