Tak - istnieje. W jakich innych czasach? Właściwie w każdym, w którym chcesz się z kimś zgodzić:
I mow the grass every Saturday. - So do I.
I liked that movie very much. - So did I.
I will tell him I don't like this. - So will I.
I have had a lot of work recently. - So have I.
I can't understand why he was fired. He had accepted the new contract. -- So had I.