Yes! You can use any good melting cheese that you like in place of the cheddar. Swiss, gruyere, gouda, fontina, or havarti are all great options. You can also swap out the parmesan cheese. I recommend replacing it with something that is also a bit sharp/salty, like asiago, feta, or even goat cheese. If you take the parmesan cheese out entirely, you will want to increase the salt a bit to make up for it.