A: I know Dr. Petter well.
B: Oh. You do?? So do I.
A: My sister plays the piano well.
B: really?? So does my sister.
A: I am in favor of her.
B: So am I.
Just two comments:
(1) Use just one question mark...?
(2) Really... needs to be capitalized (The first word, even though the word "really" is not a sentence).