Gaea should be included. Since she is an important primordial entity in the Percy Jackson universe, her presence could drive the plot. Maybe she has some unfinished business from the past that involves the primordial gods and Percy gets caught in the middle. Tartarus could also be a great character. It's a place but could be personified in the fanfiction, and Percy could have to face its terrifying power and find a way to survive or even use it to his advantage.
Erebus, the personification of darkness, would be a great addition. His shadowy nature and connection to the primordial world could create some really cool scenes. And then there's Oceanus, the primordial god of the ocean. Given Percy's connection to the sea, their interactions could be very intense and full of conflict. Percy might have to prove himself to Oceanus or face his wrath, which could be a major plot point in the fanfiction.
Definitely Chaos. As the origin of all things, it would add a whole new level of mystery and power to the story. Also, Nyx, the goddess of the night, could be really interesting. Her dark and powerful nature would contrast well with Percy's more heroic and light - hearted side.