Can this happen to superheated water?

[Superheated water](https://en.wikipedia.org/wiki/Superheated_water) refers to water that is heating well beyond its usual boiling point under extreme pressure. This cause it to display anomalous property.


I noticed that as temperature increases, so does the self-ionization of water, that is, the concentration of $\ce{H3O+}$ and $\ce{OH-}$.


It appears to me that the above phenomenon is caused by increased "freedom of movement" in hydrogen cation, or protons, allowing them to leap from one charge-neutral molecule to another, ionizing both their source and destination.


My question is, what would happen if the pressure and temperature of water is taken to the extreme? Would there be sufficient kinetic energy in the material to allow essentially free movement of $\ce{H+}$ among particles of $\ce{O^2-}$? Which makes it so that the water essentially behave like a plasma consisting of the two types of ions? Or would the energy required to reduce $\ce{OH-}$ be so enormous that some other phenomenon will take place before this is possible?


