Jun 24, Observe your dog closely for signs of intestinal upset after feeding her cheese for the first time, and consult your vet with any questions you may. Most dogs enjoy eating cheese, but is it something we should offer to our pets? Your dog's size and health determine whether you can offer him any cheese, . Aged cheeses like cheddar (including sharp and mild), Swiss and Parmesan. Find out how much and which types of cheese you can safely feed your dog. And if you're wondering if they can eat string cheese or cheddar cheese, the.