Title: Percy Jackson: Rescue Team (You can obviously change it if u want to)
Plot: Basically, Percy will quickly get bored of a regular peaceful life and will want something to do, so he'll gather some of his closest friends, Annabeth and Grover and start a rescue team. As a rescue team, people come to them with jobs for them to do, and they have to successfully complete these jobs. The jobs can be anything, like defeating a particular monster, finding a rare artifact or some object someone lost, saving someone who's in danger, things like that.
Starting: Percy, Annabeth, and Grover start a rescue team to help people out.
Over time: Throughout the story, as Percy and his team successfully complete jobs, more and more demigods, nymphs, spirits, even some monsters and gods will decide to join his team. At that point, he'll need to assess the particular job he has to do and choose who to take with him (I recommend anywhere from 2-4 other members) based on whatever the job is. For example, for a sea based job, he could go with a team consisting of himself, Tyson, Triton, and Frank.
End: You can choose the ending. One idea is that Percy gets a very difficult job (saving the world again or something similar) and after that job is finished, he decides they've done a lot and decides to retire, settling down in New Rome with Annabeth (or whoever you chose as pairing). The other idea is that there is no end, and you keep updating as you get new ideas for jobs.
Future: This can also be turned into a crossover. As Percy's team completes a bunch of successful jobs and gains fame, they start getting job requests from pantheons outside of the Greco-Roman sphere of influence. Crossover ideas are listed below.
Harry Potter Crossover Idea 1: Harry, Hermione, and Ronald have their own rescue team in England, and they hear of Percy's team based in the US. Being the top team in the UK, they decide to visit Percy's team (or you can do the other way around) and the two teams end up teaming up for a job and becoming friends and rival teams, always trying to outdo each other.
Harry Potter Crossover Idea 2: Percy gets an offer to go to the UK, where he meets Harry and the golden trio. In the UK, he joins them in their fight against Voldemort, and after they defeat him, he asks them to create a UK branch of Percy's team, to which they agree.
Harry Potter Crossover Idea 3: A particular job takes Percy to the UK, where he meets the golden trio who are just coming out of a war and want nothing more than to take some time away, maybe even leave the UK for a while. Noticing this, he asks them to come back to the US with him, where he invites them to join his rescue team. They agree, and over time, through their contacts, other characters from Harry Potter are called into the team as well.
Avengers Crossover Idea 1: Percy's rescue team draws the attention of Nick Fury, who decides that he could also make a very nice recruit for SHIELD. Percy declines the offer to join SHIELD, however, both decide that they would love to work together and form a mutual partnership, in which they call each other for help whenever needed. Through this partnership, Percy sometimes gets offers from Nick to help out with some of SHIELD'S problems, and Nick sometimes gets requests from Percy asking him to send members of the Avengers for help with certain cases.
Avengers Crossover Idea 2: The Avengers doesn't exist. Looking for things to do, the people from the Avengers go out in search of new jobs, and they all over time end up joining Percy's rescue team, where they go out on rescue jobs.
Avengers Crossover Idea 3: The avengers have been broken up. SHIELD has been put to a stop as well, and now all the old Avengers are looking for new jobs and new things to do. In search of new jobs, they all join Percy's rescue team, where he sends them on special missions. (Similar to the first one, but in the first one, SHIELD and the Avengers never existed in the first place)
Note: Keep in mind that all this crossover stuff can also be mixed and matched. You can always have the story be PJO x HP x A and add even more stories if you really feel like it (Though I feel that adding too many would make it hard to keep track of characters, team members, and would just cause confusion)
Multi-Story Series Idea: You can also turn this into a multiple story series, where the first book can be purely PJO/HOO and each future story can be a crossover, bringing HP into one story, Kane Chronicles into another, Avengers, or anything else you want.