While it can be subjected to even more extreme conditions, it doesn't "turn into" anything else in the sense of a complete transformation. It might undergo further recrystallization, becoming denser and tougher, but its basic composition remains quartz.
However, under extreme conditions of ultra-high pressure and temperature, like those found deep within the Earth's mantle, it can transform into other minerals, such as:
* Coesite: A denser form of silica, formed at very high pressures.
* Stishovite: Another high-pressure form of silica, even denser than coesite.
However, these transformations require conditions far more extreme than typical metamorphic environments. In most cases, quartzite simply becomes more tightly packed and harder under increased pressure and heat.