Boarding School books

This doesn't have a paranormal element, but the Private series by Kate Brian is set at a boarding school and is pretty good. Not as light as Ally Carter though. Wuthering High had a paranormal element, though that was more "boarding school for troubled teens" than a real boarding school. Might not be exactly what you're looking for, but those are the only boarding school ones I've read

Nightmare Academy by Frank Peretti features a boarding school - but it's not "light" YA fiction, it's somewhat dark.

As Danthia said, the PRIVATE series by Kate Brian are set at boarding school, though there is alcohol use, abuse, drug use, hazing, and murder in the series.

Also,

THE DISREPUTABLE HISTORY OF FRANKIE LANDAU-BANKS, e. lockhart (very lighthearted, about pranks and a secret society)

LOOKING FOR ALASKA, John Greene (same as above, though with death)

PREP, Curtis Sittenfeld (sex)

THE UPPER CLASS, Caroline Say, Hobson Browne, Taylor Materne (marijuana references)

A GREAT AND TERRIBLE BEAUTY, Libba Bray --this one might be closest to what you are looking for, with paranormal elements, though it's dark.

I had trouble finding lighthearted boarding school books besides the Ally Carter ones, because obviously, boarding school is a place where teens can fool around (drugs, alcohol, sex, etc.) without getting chastised by their parents, and books on this matter highlight this.