The puppy is way too young to learn the rules, you can start trying to train her by telling her NO very firmly and tapping her on the nose at the same time, also crate training. Do you have a crate for her ? Your other dogs will tell her when the biting is too sore or they dont want to play at the time, and show her who's the boss, so you shouldnt worry about that unless your other dog's seem like they will actually viciously attack her.
As for the puppy being re-homes 3 times already and she's only just over 8 weeks old, that's disgusting. She should never have been re-homed untill at LEAST 7 weeks old and made sure she is fully weened from the mother and coping on dry foods and water. Whoever had the litter and has re-homed her way too early should be reported as that is like neglect.
I love staffordshire bull terrier's and have two of my own and just had a litter of 8 puppies, that are all in there new homes and kc registered, fully vet checked, vaccinated and doing absolutely brilliant on the dry food and water. Every person who came to view the puppies were also vetted very very thoroughly before we even let them think they would be going home with a puppy. We also have everyone's names, addresses and phone numbers to be kept up do date on the puppies as they grow up.
Anyway, as I said, she is only 8 weeks old, she doesnt know right from wrong yet and wont for a while, all you can do is buy a crate, and when she bites and does anything bad then you tell her firmly NO, Bad Dog and go from there, but also when she is good make sure you praise her straight away by petting her and at the same time telling her she's a good girl.
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