Yes, but you have to store it properly. I have found still sealed packages of medium cheddar cheese that was several months old, and was much sharper than normal, although it tasted a little funny.
I don't actually know exactly how it needs to be stored, but if it's not just right, it'll mold, dry out, or rot. Mostly depending on how much moisture there is. But basically, fermentation time is all that it really needs.