i tried it and i got about 10 new floors with one dalmatian... yay XD
and i ALSO got this RADICAL item for my avatar! Green Turtleneck V2!
An easy way to get all the pieces is just keep finding new floors until you come across one that is insanely easy. Just keep replaying that over and over, it becomes tedious, but that is how I got all the avatar parts. I believe there are over 400 different parts.