To all the 2-person bands out there, add that bass or guitar to make it a three-piece. It can only make your music better, I promise.
I have a friend, really an acquaintance, who I might like, who has a 2 person band. Just drums and bass. It's called Mr. Russia. I like the music, but I'm not a fan of the vocals.
There are quite a lot of 2-piece "bands" out there, even pretty decent ones. But any band that doesn't have bass+drum rhythm section is missing out on booty-shaking grooves, and if you don't have a guitar you are probably lacking some melody.