A vapor - dwelling deity. This new god or goddess could control the very essence of vapor in the Percy Jackson universe. They might be initially neutral but get involved in Percy's adventures when they realize that the balance of the vapor - related realms is at stake.
A group of rogue demigods who have been using vapor travel to steal from other realms. They could be both enemies and potential allies depending on the situation. They might have unique powers related to vapor manipulation that Percy and his friends have never seen before.
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.
A new demigod from a really rare godly parentage, like a child of Hypnos, the god of sleep. This character could have unique powers related to dreams and illusions and could be an ally or an adversary to Percy. Another could be a centaur who has been exiled from his herd for some reason and has a vendetta against the Olympians. He could be a source of knowledge for Percy about some of the more hidden secrets of the gods.
Well, there could be new demigod children of Hades. Maybe a girl who has the power to control the shadows in a unique way, like she can use them to create portals to different parts of the underworld. Or a boy who can communicate with the dead in a more advanced way than the usual children of Hades, and he has some sort of prophecy related to Percy.
A centaur who has lived in both the Roman and Greek territories. He could be a mentor to Percy, teaching him about the similarities and differences between the two cultures' ways of combat, magic, and survival. He could also have a lot of stories about the ancient times when the two cultures were more intertwined.
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 new demigods. Maybe some who were hidden during the giant war and now come out. For example, a demigod of a less - known god or goddess.
A mermaid - centaur hybrid could be a really cool new character. This character could have the upper body of a centaur and the lower body of a mermaid. They could be an expert in both land and sea magic, and help Percy on his quests. They might also have a mysterious past that is related to the ancient wars between the gods.
Definitely Annabeth. Since she has a strong connection with Percy already, in a time travel scenario, she could be one of the main characters in the harem. Also, Piper could be there. Her charm - speak ability might play an interesting role in the harem dynamics. And perhaps some of the minor female characters from the series like Silena Beauregard could also be included if Percy travels to a time when she was still alive.
A shape - shifting creature that can take on the form of any animal. It starts off as an enemy, trying to steal something important from Percy and the Wanderer, but later realizes they are on the same side and becomes an ally. This character could bring a lot of action and mystery to the fanfiction.
A character could be a young oracle who has visions related to Percy's new adventures. She could be a bit of an enigma, not fully understanding her own powers and sometimes giving cryptic messages that Percy has to decipher. This would add an element of mystery to the story.