In some fanfictions, Percy is sent to a post - apocalyptic version of his world. He has to use his demigod skills to survive in a land full of mutated monsters. This is really exciting as it shows Percy in a completely different light, having to adapt to a world where the normal rules no longer apply. Also, there could be a plot where Percy is sent to a world where he has no powers at first. He has to regain them through a series of trials, which makes for a great character - building story.
One interesting plot could be Percy finding himself in a world where the Greek gods have different forms or powers. For example, Zeus could be a benevolent king instead of the often angry god we know. Percy would have to navigate this new world, figure out how to use his own powers in relation to these changed deities, and perhaps find a way back home. Another plot could involve Percy being sent to a world that is a blend of different mythologies, like Greek and Norse. He'd have to deal with new creatures and gods from both mythologies, which would be a real challenge.