Dermatologist
It sounds like your friend's dog may have more than just food allergies. She should see a pet dermatologist. Allergy testing can be done for contact/environmental allergies like mold, human dander, grasses etc. A better veterinarian prescription diet for food allergies is HP 19 made by Royal Canin. It is more expensive but more effective than z/d. A dermatologist will also set up a protocol for bathing and effective flea control to soothe and condition the skin and protect the dog from more serious skin infections.