
I would want the Staff to be fully mature before introducing a puppy. that would be about 3 years of age. the Pet Shar Pei I have met are not the kind to take things lying down so would be inclined to question the older dogs authority if it wasn't fully established before he is mature.
You would of course have fewer problems if your choice of companion were a bitch, but you would have to think about having one neutered. My choice would be the existing dog, as he has passed puberty, as I don't believe in spaying bitches before they reach sexual mental and physical maturity.
Even if you go for a bitch I would do as the other poster has said and establish yourself and your relationship with your boyfreinds Staffie. :D