Hi Andrew,
Thanks for your question.
While I cannot give you a specific answer for your pup, I can provide some general information on feeding veterinary diets for dogs.
When a pet is started on a veterinary diet, we typically advise not to feed other foods unless otherwise directed. This is because the efficacy of these diets may be compromised when combined with other food items. However, this all depends on the underlying reason for starting the diet in the first place and the type of diet you are feeding. Sometimes it is fine to feed other foods or supplements, and sometimes it can be detrimental. This will vary on a case-by-case basis. For example, if a pet is on a diet for allergies and is fed treats or human foods as well, it can become difficult to know if the diet is making a difference for the pet.
My suggestion would be to review everything with your vet to see whether mixing several types of foods together would be reasonable or not. Most of the veterinary diet companies offer nutrition consults to veterinarians to advise on how to appropriately feed their products.
I hope this helps.
Dr. Kim Hester