There might be new gods or minor deities introduced. They could be ones that have been forgotten or ones that are from a different part of the mythological world. Their appearance could change the power dynamics in the story. They might either help or hinder Percy in his second - chance journey.
In the 'Percy Jackson Gets a Second Chance' fanfiction, he could form stronger alliances. Maybe he'd reach out to some characters he didn't fully trust before. He could also use this second chance to get closer to his family, like his mom, and protect her better from the threats of the mythological world. He might even be able to prevent some of the major disasters that happened in the original story.
There could be a local guide in the place where Percy is exiled. This character could be an outcast from their own community and help Percy navigate the strange new land.
There could be a chaos spirit named Eris. Eris could be a mischievous character who both helps and hinders Percy on his journey with chaos. She might have the ability to shape - shift into different forms related to chaos, like a swirling vortex of dark energy.
There could be a character who is a mentor to Percy in understanding his devilish side. This character might be an ancient being with knowledge of both the divine and the demonic. For example, a fallen angel who has seen the rise and fall of many with such mixed heritages.
There could be a time - keeper character. This person or being would be an expert in all things related to time and would either help or hinder Percy in his journey with his new power. Another new character could be a time - lost hero from the past that Percy accidentally brings forward in time.
There could be a new oracle who is specifically attuned to Percy's 'son of fate' situation. This oracle might be a young demigod with unique powers that help Percy understand his fate better. Maybe they can see visions of the future that are directly related to Percy's journey.
There could be a new bully at Goode who targets Percy because he senses Percy is different. This bully might turn out to have some connection to the mythological world, like being a descendant of a minor god.
There could be a healer character. Since Percy is a broken hero, someone with the power to heal his physical or emotional wounds might be introduced. This character could have their own backstory and motives, perhaps being related to an ancient Greek deity of healing in a new and unique way.
A new demigod from a previously unheard - of god or goddess. Maybe a child of a minor deity who has some unique powers that could either help or hinder Percy in the situation of the collapse. For example, a child of Hypnos who can manipulate sleep and dreams, and their powers could be used to either give Percy visions of how to fix things or put him in a dangerous trance.
There could be ancient Greek heroes that Percy meets in the past. For instance, Heracles. Since Percy is from a different time, Heracles might not be exactly as the legends say, and they could have an interesting dynamic. Another potential character could be an oracle from an older era who has different prophecies related to Percy's situation.