so does (one)
One wants, needs, has to do, etc., something as well. A: "I need to go to the bank later." B: "So does Sarah—maybe you can share a cab with her." A: "Mommy, I want a snack, please." B: "Oh, so do I!"
so do I
1. I do too. Mary: I want some more cake. Sally: So do I. Bob: I have to go home now. Tom: So do I. Bob: Bye.