I make pizza pretty frequently, and I always have leftovers. I have a few go-to crust recipes that reheat well after being refrigerated, but I'm never happy with the cheese upon reheating. Usually I use freshly grated, part-skim, grocery store mozzarella and the leftover pizza never gets good and melty again. What other cheeses might give me better results when I reheat the pizza after a day or two in the fridge? I'm open to outside-the-box choices; I can tweak the other ingredients to complement the cheese. What I am looking for is a texture in the reheated pizza that is as pleasant (although, not necessarily the same) as it was fresh from the oven.
It isn't a perfect match for the flavor and texture of regular pizza cheese, but soy cheese (Daiya mozzarella shreds, specifically) reheats beautifully and is even good cold. We switched cheeses because of a dairy intolerance, but found the storage properties to be a great side benefit.
It does end up being a noticeable change to a pizza's flavor profile, but may be less of an impact if there are lots of other toppings on your pizza. If you find the flavor and texture of the Daiya cheese acceptable when the pizza is fresh, it will still taste the same when reheated.
While there are many cheeses to choose from, I find that provolone both heats and reheats well. Also, the flavor profile works nicely with most Italian dishes, pizza included. I've used smoked, unsmoked, mild, and sharp. Whether smoked or not, the mild tends to be a little "meltier", and more suited to the flavor I'm looking for.
I've found that lower fat cheeses tend not to reheat particularly well. Full-fat mozzarella would be better than part skim. Also, keeping the cheese in bigger chunks gives better results than shredding, so slicing may be a better way to go. I use full-fat soft mozzarella which I pull apart or slice rather than shredding, and it has a much better texture when cooled and reheated than hard mozzarella, which tends to get a waxy look and texture.
I've been thinking that the reason for this is water loss, and that the reason for the texture of shredded cheeses and lower fat cheeses after cooking is that they get dried. It may be worth trying semi-skimmed cheese in strips or thin slices and see whether that fixes your problem rather than changing cheeses. Maybe next time do half shredded, half sliced and see what you think.