Maybe they end up on a deserted island. Percy might use his skills to find food and water while Vlass tries to build a shelter. They could also encounter some strange creatures on the island.
In this kind of fanfiction, you'd have the demigods at the center. They could be new, inexperienced demigods just finding out about their powers. There would be their mentors, who might be more experienced demigods or even minor gods. These mentors could be the ones calling them during class to give advice or warn them of impending danger. Additionally, there could be other supernatural beings like nymphs or satyrs that are part of the demigod's world and are somehow involved in the events that lead to the calls during class.
One possible plot could be that a demigod is in the middle of a really boring class when they get an urgent call from their godly parent. This call could be about a new quest that they have to embark on immediately. So, the demigod has to figure out how to get out of class and start the adventure without raising too much suspicion among their mortal classmates.
Another option for the main antagonist could be a spirit of an ancient Greek scholar who was banished from the world of the gods. This spirit haunts the Greek class and tries to possess Percy because he sees Percy as a way to get revenge on the gods. It causes chaos in the class, making it difficult for Percy to focus on his studies and also putting his friends at risk.