Move to combat.
Helm of the Host will trigger and create a copy of Identity Thief.
Attack with the Identity Thief token, triggering it and exiling Medomai the Ageless until end of turn.
the Identity Thief token will deal combat damage as a copy of Medomai the Ageless, granting you an extra turn.
At the end of the turn, Medomai the Ageless returns to the battlefield.
Sacrifice the token.
Repeat for infinite turns.

Infinite turns

Medomai the Ageless

Identity Thief

Helm of the Host

Declare Identity Thief as an attacker.
Identity Thief triggers, exiling Medomai and causing Identity Thief to become a copy of Medomai until end of turn.
Deal combat damage to an opponent using Identity Thief.
Identity Thief triggers, causing you to take an extra turn after this one.
At the beginning of your end step, Identity Thief triggers, returning Medomai from exile to the battlefield.
During your cleanup step, Identity Thief stops being a copy of Medomai.
Repeat each turn.

Sakashima of a Thousand Faces

Mirror Box

Declare Identity Thief as an attacker.
Identity Thief triggers, exiling Medomai the Ageless, becoming a copy of it until end of turn and Return Medomai from exile to the battlefield at end of turn.
Deal combat damage with Identity Thief, causing you to take an additional turn after this one.
Activate Crystal Shard by paying {U} and tapping it, returning Identity Thief from the battlefield to your hand.
Cast Identity Thief by paying {2}{U}{U}.
At the beginning of your end step, Identity Thief triggers, returning Medomai from exile to the battlefield.
Pass the turn.
Repeat.

Crystal Shard

Declare Identity Thief as an attacker.
Identity Thief triggers, exiling Medomai and causing Identity Thief to become a copy of Medomai until end of turn.
Deal combat damage to an opponent using Identity Thief.
Identity Thief triggers, causing you to take an extra turn after this one.
At the beginning of your end step, Identity Thief triggers.
Holding priority, activate Identity Thief by paying {1}{U}, blinking it.
Identity Thief enters the battlefield, triggering Deadeye Navigator's soulbond ability, repairing Identity Thief and Deadeye Navigator.
Resolve the Identity Thief trigger, returning Medomai from exile to the battlefield.
Repeat each turn.

Deadeye Navigator

Declare Identity Thief as an attacker.
Identity Thief triggers, exiling Medomai the Ageless, becoming a copy of it until end of turn and Return Medomai from exile to the battlefield at end of turn.
Deal combat damage with Identity Thief, causing you to take an additional turn after this one.
At the beginning of your end step, Identity Thief triggers, returning Medomai from exile to the battlefield.
Pass the turn.
Repeat.

Mirror Gallery

Declare Identity Thief as an attacker.
Identity Thief triggers, exiling Medomai the Ageless, becoming a copy of it until end of turn and Return Medomai from exile to the battlefield at end of turn.
Deal combat damage with Identity Thief, causing you to take an additional turn after this one.
Activate Erratic Portal by paying {1} and tapping it, returning Identity Thief from the battlefield to your hand.
Cast Identity Thief by paying {2}{U}{U}.
At the beginning of your end step, Identity Thief triggers, returning Medomai from exile to the battlefield.
Pass the turn.
Repeat.

Erratic Portal

Pay {3} and tap Mimic Vat to create a copy of Identity Thief with haste.
Attack with the Identity Thief token, triggering it and exiling Medomai the Ageless until end of turn.
the Identity Thief token will deal combat damage as a copy of Medomai the Ageless, granting you an extra turn.
At the end of the turn, Medomai the Ageless returns to the battlefield.
Sacrifice the token.
Repeat for infinite turns.

Mimic Vat

Declare Identity Thief as an attacker.
Identity Thief triggers, exiling Medomai and causing Identity Thief to become a copy of Medomai until end of turn.
Deal combat damage to an opponent using Identity Thief.
Identity Thief triggers, causing you to take an extra turn after this one.
At the beginning of your end step, Identity Thief triggers.
Holding priority, activate Eldrazi Displacer by paying {2}{C}, blinking Identity Thief.
Resolve the Identity Thief trigger, returning Medomai from exile to the battlefield.
Repeat each turn.

Eldrazi Displacer

Tap Kiki-Jiki to create a copy of Identity Thief with haste.
Attack with the Identity Thief token, triggering it and exiling Medomai the Ageless until end of turn.
the Identity Thief token will deal combat damage as a copy of Medomai the Ageless, granting you an extra turn.
At the end of the turn, Medomai the Ageless returns to the battlefield.
Sacrifice the token.
Repeat for infinite turns.

Kiki-Jiki, Mirror Breaker

Declare Medomai the Ageless and Felhide Spiritbinder as attackers.
When Medomai the Ageless deals combat damage to a player, it triggers, causing you to take an extra turn after this one.
When Felhide Spiritbinder untaps in your next extra turn's untap step, it triggers, allowing you to pay {1}{R} to create a token copy of Identity Thief with haste.
Declare the Identity Thief token and Felhide Spiritbinder as attackers.
The Identity Thief token triggers, exiling Medomai the Ageless, becoming a copy of Medomai the Ageless until end of turn, and creating a delayed triggered ability.
When the Identity Thief token deals combat damage to a player, it triggers, causing you to take an extra turn after this one.
At the beginning of your end step, the delayed triggered ability from step 5 triggers, returning Medomai the Ageless from exile to the battlefield.
Let the Identity Thief token die to the legend rule.
Repeat from step 3 each turn.

Felhide Spiritbinder

Pay {2}{R} and tap Feldon to create a copy of Identity Thief with haste.
Attack with the Identity Thief token, triggering it and exiling Medomai the Ageless until end of turn.
the Identity Thief token will deal combat damage as a copy of Medomai the Ageless, granting you an extra turn.
At the end of the turn, Medomai the Ageless returns to the battlefield.
Sacrifice the token.
Repeat for infinite turns.

Feldon of the Third Path

Tap Identity Thief to create a copy of Identity Thief with haste.
Attack with the Identity Thief token, triggering it and exiling Medomai the Ageless until end of turn.
the Identity Thief token will deal combat damage as a copy of Medomai the Ageless, granting you an extra turn.
At the end of the turn, Medomai the Ageless returns to the battlefield.
Sacrifice the token.
Repeat for infinite turns.

Combos with "Identity Thief"