Should I get a submissive Miniature Pinscher or a dominant one?

My dog is a medium/large sized 4 year old mutt (im thinking pitt bull and rhodesian ridgeback) BUT he is extremely submissive and even does the whole laying on his side with his ears back thing when he sees youre showing dominance towards him. he would never do harm to the other dog and really doesnt even play with other dogs for some reason.. so im not worried about him accidentally hurting the smaller one. so what do you think? dominant? submissive? or should i not get a min pin.. are they not the best breed to be put with this kind of dog? thanks