Have you ruled out environmental allergies?
As far as diet, the best thing is to find a novel protein and carb/starch source to identify if there is an allergy to one of the main ingredients. It is also a possibility that a dog can be allergic to the vitamin packs added to kibble. It's a lengthy process trying to rule out which foods could be causing the sensitivities but a dermatologist will tell you that the best way to determine a food allergy is by an elimination diet...don't waste your money on a blood serum test! They warned me not to but I did it anyway and I wish I hadn't. The results showed she was allergic to everything she was currently eating but did not show an allergy to chicken which I know she has an allergy to. If you are testing for environmental allergies, go to a derm and ask them to do the skin test. It's considered to be the gold standard for allergy testing. Again...I wish I would have done that. You live and you learn.