Have you seen the play?SO have I

"She has three dogs." "So does he."
Or should we use "So has he" - 'does' is more colloquial,casual,and 'has' is just a little bit more formal in speech.
I have also heard that to a sentence "I've got a dog." we reply "So have they" because "have" is an auxiliary verb here.-yes - or,"So do they."
The same as in a sentence "She has never been to Rome." "Neither have I." Am i right?Yes - that is the correct reply请问那是对的还是错的