I was playing Midweek Magic Jump In with the new Aetherdrift cards. My opponent had a Greenbelt Guardian on the battlefield. They were able to use its Exhaust ability multiple times and it was an 11/11 having Exhausted three turns in a row. From what I could tell they had no card in play that granted multiple uses of the same Exhaust ability. Their Greenbelt Guardian was not leaving the battlefield and coming back.

I have only played against that card once so far, and I have not used it, so I can not say if this can be replicated.

I play on iOS using Epic Games.