Is there a method that I could find as many values as I want for variables $w, x, y, z$ so that the equation $x^w+\sqrt[w]{y}=wz$ satisfies?

I found $(2,3,9,6)$ ; $(4,2,0,4)$ ; $(-2,1,1,-1)$ and $(3,1,8,1)$, but I'm sure there are much more than this.

**EDIT:** I forgot to add that I want solutions so that a value doesn't repeat more than twice.