When I first became acquainted with the Harry Potter stories (via the movies, not the books), I was struck by the resemblance to some of my favorite classic series. Not the Lord of the Rings, Narnia, or George MacDonald, but rather the many college series from the early twentieth century.
Those followed a young man or woman through college, and sometimes saw them past it. While the stories weren't about magic, they had eccentric professors, sports rivalries, good friendships, and in some cases, exploits against criminal elements.
For example, the Betty Wales series (written by Edith K. Dunton as Margaret Warde, published between 1904 and 1917), contained the following titles:
Betty Wales, Freshman
Betty Wales, Sophomore
Betty Wales, Junior
Betty Wales, Senior
Betty Wales, B. A.
Betty Wales & Co.
Betty Wales on the Campus
Betty Wales Decides
The books relate each year of Betty Wales' terms at college, and then for a time follow her adventures beyond college. There's no arch villain to be defeated, but the stories are still fun.
Underneath the wizarding world, the Harry Potter stories thus seem a direct descendant of the classic juvenile college series. The framework is there; J. K. Rowling just added her own magic.