All white cats are not prone to itching in one spot. He may stop because it becomes too painful
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Can you see any blackheads on his chin?
Changing his food to a quality grain free will only benefit your cats. They are carnivores, not omnivores. Cats have a very highly unforgiving digestive system, unlike dogs, or humans, their requirement is quite exact.
Genetics can play a huge roll in how our bodies react to different things, including allergies. There is no harm in changing his food to see if it works, if not, a trip to the vet to get a skin scraping may answer your question.
The two that I have used with Jasper to get him to stop are:
Wellness, grain free and Nature's Variety Instinct. Both are good foods. My cats prefer the Instinct, but there are others that prefer Wellness.