Cast Exchange of Words by paying {1}{U}{U}.
When Exchange of Words enters the battlefield, it triggers, exchanging the text boxes of Medomai and Mistmeadow Vanisher until Exchange of Words leaves the battlefield.
Declare Medomai as an attacker.
Medomai triggers, exiling Exchange of Words until your end step.
When Exchange of Words leaves the battlefield, Medomai and Mistmeadow Vanisher retain their original textboxes.
Deal combat damage using Medomai.
Medomai triggers, causing you to take an extra turn after this one.
At the beginning of your end step, Medomai triggers, returning Exchange of Words to the battlefield from exile.
When Exchange of Words enters the battlefield, it triggers, exchanging the text boxes of Medomai and Mistmeadow Vanisher until Exchange of Words leaves the battlefield.
Repeat from step 3 each turn.

Infinite turns

Medomai the Ageless

Exchange of Words

Mistmeadow Vanisher

Cast Metamorphic Alteration by paying {1}{U}, attaching it to Medomai, naming Mistmeadow Vanisher and causing Medomai to become a copy of Mistmeadow Vanisher.
Declare Medomai as an attacker.
Medomai triggers, exiling Metamorphic Alteration until your end step.
When Metamorphic Alteration leaves the battlefield, Medomai is no longer a copy of Mistmeadow Vanisher.
Deal combat damage using Medomai.
Medomai triggers, causing you to take an extra turn after this one.
At the beginning of your end step, Medomai triggers, returning Metamorphic Alteration to the battlefield from exile attached it to Medomai, naming Mistmeadow Vanisher and causing Medomai to become a copy of Mistmeadow Vanisher.
Repeat from step 2 each turn.

Combos with "Mistmeadow Vanisher"