I had adopted a senior cat who had terrible digestive problems, was always hungry but food passed right through him. I thought it would be a hospice situation. but I took him to my vet who immediately said a lot of cats (possibly dogs as well) develop sensitivities/allergies to chicken, which are basis of many foods and treats. He switched him to prescription venison based food (simple formula with just venison and pees) . Within a couple of days stomach improved, slowly weight gained and fur grew back. after 6 months to a year I was able to try a few other things on a limited basis (beef, fish based) but no chicken or poultry.
Might discuss this with your vet. I was also able to feed slightly less expensive Instinct brand venison (97%) with success which he liked better than canned prescription venison which was quite dry. Ironically he liked the dry prescription food with venison (DD?).
Good luck and thanks for adopting older gent,
#PetHealthandNutrition