Another favorite young adult series of mine is Maximum Ride by James Patterson. The story is about Max, a girl of 14 who is surrounded by her 5 friends - all who can fly. Literally. Granted this series has not much to do with Greek mythology, but something about it all reminded me strong about Percy and his group of friends who are always in trouble and always manage to become the heroes somehow.
I do love all James Patterson's novels, and this is in fact the first series written for young adults that I've read by him (I'm mostly enjoying his Alex Cross series and the Women Murder Club series). So when I started with this teen series based on a friend's recommendation, I was not quite sure what to expect.
I do still find traces of James Patterson's writing style, but it is indeed a genre of its own. Basically the story follows the 6 kids who are fleeing for their lives, who have no idea what happened to them, why they have wings and how is it that they can use them when the need comes up. They're apparently part of a genetic experiment gone wrong, where they escaped and are running literally for their lives.
Just like Percy and friends, they are also fighting evil - this time in terms of solders looking like werewolves. The pace is fast, the story gripping and you'll soon end up rooting for the kids.
Currently there are 8 books in the Maximum Ride series.
Btw, speaking of being part of an experiment and kids fleeing, you might also want to look into The Maze Runner teen series - it doesn't remind me so much of Percy Jackson, as much as of Maximum Ride, so keep this in mind in case later on you'll be looking for more books like Maximum Ride.