Of course we can!
Oh, this'll be sooo much fun!
It reminds me of a game I used to play called monsters. 3-4 players, pens/colours/paper. Each person draws a monster head however they want and then they fold it over so only a part of the bottom (maybe a neck) can be seen. They pass it around, and the next person draws the body and arms, folding it so only the pelvis or whatever shows and passes it along. Next person draws the legs, passes it back to the originator (or 4th person) who then names it. On the count of 3, everybody unfolds the paper and sees the wacky creations they've made.
Edit: And for our games, we can use this to name it: http://norefuge.net/vgng/vgng.html