There's no way to break it in standard, but in extended, you can copy the extra turn ability with Rings of Brighthearth which would allow you to go infinite.
That's not enough. Look what happens in a turn-by-turn breakdown. Note that the turns are labelled relative to the loop, not by the actual turns taken in game.
T1: Magosi tapped for extra turn. Copy w/ Rings. Replay Magosi (ETBT)
T2: Extra Turn #1: Tap to load Magosi.
T3: Extra Turn #2: Skipped for Magosi
---: Opponent goes.
You can get 2 turns for every 1 the opponent takes, but you need two copies of Rings to make this truly infinite. Technically Magosi + Rings + Amulet of Vigor (or Liquimetal+Key) works, but that probably isn't gonna cut it, even in Standard.