This is a really clever idea. I like how it plays out in a variety of different environments, leading to all sorts of wacky puzzles with a crazy variety of objects (possessing a fire? possessing a painting? possessing the salt? I love it!). I played it through to the end, and I particularly enjoyed the cooking puzzle in the last level.
It also works really well with the color scheme. Neutral objects are white, gray, and black; possessable objects are red; currently possessed items are blue.
There are a few issues, though. For one, the controls feel very stiff, making it somewhat tedious to do certain jumps. In the first few levels, the frogs have a tendency to fall through the floor, making it impossible to win the level. Also, not all objects change to blue when possessed (e.g., the lawnmower), and not all objects change back to red when you un-possess them.
Finally, there is no sound. It seems like a small thing, but it really adds a lot of depth of feeling to a game.