Well, a plot could involve the dragon being cursed. Percy discovers the dragon in a weakened state. The curse is related to an ancient grudge between two minor gods. Percy has to journey to find these gods and convince them to lift the curse. Along the way, he faces challenges like the dragon's uncontrollable outbursts which put him and his friends in danger. Or perhaps the dragon has a hidden lair filled with treasures that are actually powerful artifacts. Percy has to enter the lair, deal with the dragon's defenses, and retrieve the artifacts to stop a dark force from using them.
One idea could be Percy having to form an unlikely alliance with the Dragon King to defeat a common enemy, like a new and powerful Titan. The Dragon King might have his own motives and secrets that Percy has to figure out during their partnership.
One plot idea could be Percy having to team up with Hera to rescue a group of demigods who have been captured by an ancient monster. Hera, despite her usual aloofness, realizes she needs Percy's unique skills.
One unique plot idea could be that Percy discovers he has a special connection to the dragons because of his demigod powers. Maybe he can communicate with them on a deeper level than others. Another idea is that the dragons are the key to solving a new threat to the demigod world, like a powerful ancient evil that only the combined strength of the demigods and the dragons can defeat.
One idea could be a crossover where Harry and Percy meet during a magical event that blurs the boundaries between their worlds. Maybe a powerful dark force is causing chaos in both the wizarding world and the demigod world, and they have to team up to stop it. They could share their unique magical abilities and learn from each other's fighting styles.
A great plot could involve Percy being sent on a quest by a primordial. Since primordials are so powerful and ancient, the quest would likely be extremely dangerous and full of unknown challenges. For example, he might have to retrieve an ancient artifact that was lost in the time before the gods. This could lead to Percy facing not only physical challenges but also moral dilemmas as he deals with the primordial's motives.
A plot could involve Hera taking Percy on a journey through the past to show him the origins of the gods' power and how it relates to the current problems in the demigod world. This would give Percy a new perspective and knowledge that he can use to save the day. Or perhaps Percy accidentally stumbles upon a secret of Hera's that she's been hiding for centuries, and she has to enlist his help to keep it safe, all while other gods are trying to uncover it too.
One idea could be Percy gets cursed by Circe to forget his friends and mission, and he has to struggle to regain his memories while under Circe's influence. Another could be Circe teams up with Percy to fight a common enemy that threatens both the mortal and magical worlds. Or perhaps Percy has to rescue his friends from Circe's island after they are turned into animals, but he discovers that Circe has a more complex backstory and motives than he thought.
A great plot could involve Percy going on a quest not for the typical reasons like saving the world or a camp, but to find a way to restore the memories of a friend who has lost them due to a powerful spell. Along the way, he discovers secrets about his own past that were hidden from him. He might also encounter new demigods with unique powers who either help or hinder his journey.
One idea could be that Padme somehow gets transported to the Percy Jackson universe. She could use her diplomatic skills to help resolve a conflict between the demigods and a new, powerful enemy. Maybe she teams up with Percy and they combine their unique abilities to defeat the foe.
One idea could be Percy getting a magical haircut that gives him new powers. Maybe the hair is cut by a special sword and as each strand is cut, a new ability like controlling water in a more unique way or being able to communicate with sea creatures better is bestowed upon him.