The Colors of the Sky-supplement also has mouse, wolf, horse (or rather pony), fish, and for those wanting to play humans, witch.

But if we're going to add possums and the like, we probably should go without rules, though the books are good guidelines for how characters may act. Besides facts, looking for associated folklore and popular culture on possums would probably be helpful in developing the personality traits and skills of the character.

Although a little personal twist in character shouldn't hurt too much. I was thinking that my character is a dog, who spends his days with the family's littlest ones watching Paw Patrol (or whatever this world's equivalent to it is) and other pre-school edutainment shows. As such when he transforms, his "clothes" are like those of a superhero, and his actions take heavy inspiration from the shows the children watch. He sings, uses catchphrases, quotes and in general acts over the top. He may grow out of it, or go in his own direction, depending on where the story goes.