My DD12 finished reading the Percy Jackson series... 3-4 times already.
She doesn't want to start the Red Pyramid until more books are out because she just...can't...wait...to read the next book in a series.
She'd rather re-read the PJ series again and AGAIN. She made her sister (10) read the series also so they can discuss. And she reads the fanfiction about PJ on-line.
She has the Kingdom Keepers and the Harry Potter books ready to read but hasn't started them yet.
According to her, she like Mythology but not "Magic" or "Fantasy" books.
She did finish the How to Train a Dragon series because that was super easy and fast to read.
I told her that if she finished the HP series I would take her and her sister to US/IOA.
And if she started another series, I would read the PJ series also.
There's just no substitute for her, she LOVES the series.
Good luck with finding a new series!
I did borrow the 39 Clues book by Rick Riordan from the library for her and her sister a while ago and neither was particularly interested in the book or series at the time. But that was a while ago before she fell in love with the PJ series.
So, maybe I'll borrow it again along with the second book in the series and see it they can get into them now...
Good luck.