I am wanting to run an adventure that involves lots of high fantasy and magic.

This game will have knights, dragons, princesses, wizards, liches, etc.

The tricky part is that I want the rules flexible enough to handle strange faerie tale style magic. This should include drastic changes to characters such as changes to abilities, classes, even race and species tranformations.

If there a game that can can handle this?

Something like FATE. PbtA, OVA. There's likely a whole lot more.

For mid crunch, I highly recommend BESM of any kind, Preferably 3.
And although I quit playing GURPS a couple years ago, if crunch is no issue, their flexibility is through the roof. Crunch is very high with them though.