Another plot could involve a new threat emerging that is related to the events of 'The Last Olympian'. Say, some ancient power was awakened during the big battle but no one noticed at the time. A group of demigods, led by Percy, has to figure out what it is and how to stop it before it's too late. They might have to journey to some long - forgotten places and face new monsters along the way.
Percy Jackson himself is very popular. He's the main character of the series, so fans often like to continue his story, explore his relationships further, or put him in new and challenging situations. His powers and his journey are really interesting to build on.
In this kind of fanfiction, one possible plot could be Percy having to deal with the politics among the Olympian gods. He might try to bring about changes, like making the gods more involved in mortal affairs in a positive way. For example, he could convince them to be more proactive in protecting the environment which is being damaged by humans. Also, Percy would probably have to face new enemies. Since he's now an Olympian, he could attract the jealousy of some minor gods or ancient monsters who see him as a threat to the established order.
One of the main themes is heroism. Percy has to face numerous challenges and overcome them, showing what it means to be a hero. Another theme is friendship, as Percy and his friends rely on each other throughout their adventures. Also, there's the theme of identity, with Percy trying to figure out his place as a demigod in the world of the Olympians.
One popular Percy reading The Last Olympian fanfiction is 'The Aftermath' on FanFiction.net. It delves deeper into Percy's thoughts and experiences after the events of the book.
Another great thing is that it allows for crossovers. Maybe Percy reads The Last Olympian and then somehow gets transported into the world of the book in the fanfiction. This can lead to really exciting and unexpected plotlines. It can also bring in characters from other related fandoms and create unique interactions. It gives fans a chance to explore 'what if' scenarios that they might have been thinking about while reading the original book.
Well, one possibility is that they might initially be cautious of each other. Percy, being from the Greek side, and Jason, from the Roman side, have different upbringings in their respective demigod cultures. But they could quickly realize they have a lot in common, like their leadership skills and their powerful abilities. They might end up teaming up to face a new threat that emerges, combining Percy's control over water and Jason's control over the wind and lightning.