Given that this thread is all about who wins between Yog and Multi-Eternity though, I'll just say my opinion there before I leave.
Yog-Sothoth is a being who embodies everything in his verse save for Azathoth ("allied to reality's whole unbounded sweep", "All in One and One in All", being the "SUPREME ARCHETYPE" [caps was Lovecraft, I'm just quoting]), including the other Outer Gods, all of whom are beings several layers of infinite voids beyond time and space (that's from Hypnos) and time and space is infinite dimensional (that's from through Gates of the Silver Key).
Meanwhile, Multi-Eternity is an infinite dimensional being who embodies a really really really huge infinitely dimensioned multiverse - but he's not actually anywhere more than that.
People here seems to love their dimensional tiering from what I've seen, so I'm willing to bet that people here would say a 6D being who controls a 6D universe wins over a 4D being who controls with a constantly multiplying infinite 4D multiverse. So under that logic, I see nothing wrong with saying that a being who is several layers beyond infinite dimensions wins over a being who is only infinitely dimensioned, no matter how powerful that infinitely dimensioned beings.
That's my piece. I'm out.