I think I've been there done that with our Pit depending on the liver problems. Years ago he had a liver imbalance(numbers??) and was put on Sam-e pills. I've continued giving him at a lesser dose of the supplement after he was cured for most of his 12-13 years with no further problems. As per the Vet food, have you read the ingredients? I'm a label reader and Costco has better food. The Vet gave me samples of prescription dry & canned weight loss food that our Rottie wouldn't eat. You have to understand, she will gobble anything that isn't moving, including plastic flowers. How about canned food? IMO, garbage. Again, ingredients. "Tastes like filet magnon"? You can feed him trimmed chicken for less cost, though some cooking time. Feeding him four times a day, no wonder he isn't ready to eat a standard meal. Just my opinion, but if your Vet is treating the liver problem with "prescription" food that he sells, I'd get another vet..
In my opinion only.... Good luck.. :)