My cat is chewing his back feet and parts of his front paws until they are raw and bleeding. I have taken him to a vet and pet pharmacist with no luck of an answer. Any suggestions?

I'd suggest a new vet - honestly.  There's always a reason for this to happen.  If the usual testing and checking for mites, foreign objects, allergies etc have been done with nothing showed up then it could just be a habit the cat picked up.  Some pets will lick to relieve boredom, tension etc like us adults do things like bite fingernails or play with hair and stuff.  But with animals this habit often develops into lick sores, which make them lick even more.  Your vet should be concerned and treating.  I really would find another vet.If your cat doesn't go too crazy with a cone collar on until you can get her to a vet that might help it from getting worse.  You may want to try some shredded paper in her litter box (or organic litters if your area and budget allow for it) until it gets treated, as the litter in the box could further the discomfort and possible infection.

Your kitty may be pruritic (very itchy) and can have a number of underlying causes from allergy to infectious causes to neoplasia. Your cat could be self mutilating for some reason and is often brought on by stress and your kitty maybe being a little obsessive compulsive. Some cats will begin that sort of behavior due to matting as well since it is irritating and painful, if you have a long haired cat it may be there is matting in between the toes or pads and it is irritating them (and all the chewing can make it worse) and a trip to a groomer who is experience in cats can help get rid of matting and excess hair. It could have been a minor irritation and all the licking your kitty did is causing further irritation as said. It could even have a root in a neurological problem.
I was going to try and look up any clinics that specialize in and are geared to cats in your area but have no idea where you live so you may want to look into that since they are likely to have more experience with some of the more elusive issues cat's can suffer from as well as more common problems.  I hope you get it figured out and your baby is feeling better very soon.
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