Has anyone ever had their cat’s allergies tested or had immunotherapy injections?

I know this would not be cheap, but the vet’s inclination to jump on Chicken, seems like an easy out. I have multiple cats that eat multiple foods and they never agree on anything. I have bags of food upgrade failures. So changing food is nice in theory, but it’s easier said than done. The vet said the kitty with the allergies had higher eosinophils, but that doesn’t tell me the why. It could even be an environmental issue, as the air purifiers have been off lately. I have seen that some vets go beyond the Chicken story, but maybe this is only the bougie clinics.

I’m trying some LiveClear food to see if that helps the allergy kitty. I also have plans to build some upgraded air purifiers, but they are not kitten friendly, which is why the one air purifier is down temporarily. On the bright side, someone is eating the expensive Duck food, but I suspect it’s the kitten. I need to get the food cam installed.