Hey, not sure if you're still looking for new books. I've got quite the list of things I can think of. Here's some that you may or may not have read that I personally absolutely loved. They all definitely have more than one book to them, though some of them might actually be hard to find because they're not entirely popular. I'm listing the first books of each series:
The Lost Years of Merlin by T.A. Barron
The Frog Princess by ED Baker (Don't think of that one movie, this is a different setting with different characters and different plot)
Dragon Slippers by Jessica Day George
The Ranger's Apprentice: Ruins of Gorlan (though that was said)
Artemis Fowl by Eoin Colfer
The Alchemist by Michael Scott
Eragon by Christopher Paolini
Inkspell by Cornelia Funke
I know you said that you prefer a story with more than one book, but
Dragon Rider by Cornelia Funke
I read that book many times.
Well there you go, a whole dump of books that I thought of.
Basically, if there's medieval and/or magical elements involved, I will read it.
And if you've read all these books already then wow. Because 90% of the time, people won't know what some of these books are when I mention them, even the heavy readers. xD
The Frog Princess series was my childhood favourite. I still love it. I checked them out from my library, and the librarian even let me keep one of the books because I read it so much and they were about to withdraw it xD