It's not likely that the actual Olympus (in the context of the Percy Jackson series being a place of the gods) reads fanfiction. Fanfiction is a creation of the fans in our world, and there's no indication in the books that the gods or Olympus as an entity would engage with it.
One possible reason could be that Percy feels betrayed by the Olympians first. Maybe he discovers some dark secrets about them that make him lose faith. For example, if he finds out that they have been using demigods unfairly in their battles or politics.
If Olympus read Percy Jackson fanfiction, the gods might be either amused or offended. Some fanfictions might portray them in a way that they don't like, and they could potentially take revenge on the author (if they could reach our world). But on the other hand, they might find some of the creative interpretations quite funny.
A new and powerful Titan who has been hiding and gathering strength all this time. He could be jealous of the Olympians' power and wants to take over. Percy would have to figure out his weaknesses and stop him before he causes too much destruction.
Percy himself is always interesting. In fanfiction related to The Staff of Olympus, he might have new challenges and growth. Another is Annabeth. Her intelligence could be used in unique ways to figure out the mysteries of the staff. Grover can also be really cool as he might use his nature - related powers in unexpected ways in relation to the staff.
In fanfiction, if Percy Jackson takes over Olympus, he might bring a new order. He could reform the archaic rules of the gods. For example, he might ensure fairer treatment of demigods, like better training and protection. Also, he could change the power dynamics among the gods, making them more accountable for their actions.
In some 'Percy Jackson Raised on Olympus' fanfictions, there could be a plotline about Percy uncovering long - hidden secrets of Olympus. For example, he might discover a forgotten prophecy that has implications for the entire pantheon. Also, his interactions with the nymphs and other mythical creatures in the Olympian realm can make for an exciting story. Maybe he has to protect them from a new threat that is emerging within the boundaries of Olympus itself.
Well, usually it starts with Percy having some sort of conflict with the Olympians. Then he starts to make plans in secret. He might gather a group of supporters, like other disgruntled demigods or even some mythical creatures who also have a grudge against Olympus.
One idea could be Percy going on a quest to find a lost artifact that has the power to restore a dying part of the godly realm. This would involve him facing new monsters and making unexpected alliances.
One idea could be exploring a new prophecy that involves Percy and his friends having to team up with some of the lesser - known gods. This would introduce new characters and powers into the story.