Quoted By:
Thinking about potential divine transformations for Chaya now that she's lost her tail and I wanted to air my thoughts.
As I understand it Super Saiyan God, despite the name, actually has nothing to do with the golden Super Saiyan forms. It's just called that because Saiyans are uncreative. The red hair, eyes and aura are the result of the natural Saiyan god ki. The pure version.
Ultra Instinct appears to be what happens when you use Super Saiyan God with Angel ki instead of natural Saiyan god ki, resulting in a much more powerful variant of the transformation. The form itself is a shortcut that Goku created instead of learning the actual technique the normal way, which we see him do later in the manga. Applying the principles of Ultra Instinct to his lower forms without the massive power boost.
Ultra Ego appears to be the same thing but for Destroyer ki. A mutation of Super Saiyan God that Vegeta created as a shortcut to learning the actual technique the normal way, which we again see him do later in the manga. Which is funny considering Goku was able to pull off a Hakai ages ago in the manga against Fused Zamasu.
In theory you should be able to combine these with Super Saiyan the same way they can with regular Super Saiyan God, but that's going to be impossible until Goku and Vegeta have actually mastered these forms.
Following this trend, there should be a mutation of Super Saiyan God based on Kaioshin ki. We've never seen that in any official material, but we do see what happens when you combine it with Super Saiyan. That being Super Saiyan Rose. We just don't know what technique forms the basis of it.