Interesting, Silmiel, I didn't know that Nicholas Flamel was a real person! My respect for JK Rowling just increased a notch.
Back to the original question: "Could Middle-earth be more magical than it already is?" Well, as someone said already, there are different types of magic. There's the HP-style, wave your wand and say a couple of magic words and get instant results type of magic, and then there's the magic of Gandalf's intagible inner power, and there's the magical power of Saruman's voice... etc etc.
As I see it, the magic of Harry Potter is more fanciful. The magic of the Lord of the Rings is more subtle but so much more powerful. I mean, come on. Gandalf would so own Dumbledore in a fight. Or he could pull his Denethor moves and just bludgeon Dumbledore to death
(Such a massive departure from the book but amusing all the same
)