Chandler, I also don't understand what you mean by saying that "gotten" is plural. Also, it IS grammatically correct in American English. Finally, "modern English" means the English language from about 1500 until now, and "gotten" was grammatically correct in Britain at some point between then and now. I think you mean "contemporary British English", not "modern English".
I'm sorry, Chandler, I don't know exactly where in the British Isles "gotten" originated, but in the course of my graduate studies in English Literature, I had multiple (British and American) professors who referenced, mentioned, or noted "gotten" as a part of speech that had once been "British English". There was never any debate or ambiguity or doubt about that point; it was mentioned in passing as a matter of course. It came up mainly in discussions about specific bits of Elizabethan literature, such as Shakespeare, Christopher Marlowe, etc. I don't know if it was widespread before/after the Elizabethan era, but I'm going to find out.