Ultra high pressure supersolid helium

[andrew848]

TL;DR

I was wondering what would happened if you cooled helium to near absolute zero and kept pressurizing it.

Assuming you could get around the material and engineering problems with anything at high pressures what would happen if you kept pressurizing helium past a super solid state. If the pressures where high enough would you have a similar effect to metallic hydrogen with it behaving as a degenerate gas with superfluid and superconductor properties?

 

[cmb]

There is a phase diagram of helium 4 here
https://i.stack.imgur.com/pymYA.jpg
I presume all materials become 'metallic' at some pressure (possibly not fermions like He-3??), the question is what that pressure is predicted to be and if there is ever a physically real situation where it might get there?