While it is possible to breed an American bulldog and a Staffordshire bull terrier together, the resulting puppies would not be considered to be purebred pit terriers. They would be considered to be a mixed breed or "designer dog." The puppies would likely inherit some of the physical characteristics and temperaments of both breeds, but they could also display traits that are unique to their individual personalities.
It is important to note that any hybrid or designer dog can be unpredictable in terms of temperament and appearance. It is always recommended to do your research and talk to a reputable breeder before bringing any puppy home.