I don't necessarily have any specific ideas, but I can think of some questions to ask yourself:
- How much do the worlds interact with each other? Are some of them friendly or hostile toward other worlds?
- Why does the cat want these gems? Do they enable access to more worlds? Are they used for some kind of weapon to fight the aliens?
- Does having more gems give the player access to more power-ups?
- Do the aliens know about Doc, the cat, or the gems? Do they have some of the gems? (This would provide a logical reason for boss fights.)