Can dogs be allergic to cats?

The vet did blood work on my 4 year old Boxer Bruno, he said Bruno had very bad allergies but was unable to pinpoint what they were. I have him on very good dog food (neutrena), hes up to date on all vaccines, been neutered, and is in good health. But his eyes and nose are always runny. I even bought an expensive air purifier. Does anybody know if a dog can be allergic to a cat?