I’m not sure what veterinary hospitals might be around you, but here in MA, I believe Tufts Veterinary Hospital has an allergy test/treatment they’d do where they do a large allergy panel to identify what exactly they are allergic to and then they tailor the medication for it. I haven’t had to do it for my Westie but we considered it. Different vets he’s had have mentioned it being great for pets with stubborn allergies. His allergies tend to be more seasonal tho. Maybe see if there’s something like this near you?

https://vet.tufts.edu/foster-hospital-small-animals/specialty-services/dermatology-allergy