Declare a creature you control that cannot be blocked by an opponent as an attacker.
Holding priority, activate Brass Squire by tapping it, attaching Assimilation Aegis to the attacking creature.
Assimilation Aegis' second ability triggers, causing the creature to become a copy of Medomai the Ageless.
Deal combat damage with the creature.
The creature triggers, causing you to take an extra turn after this one.
Move to your next turn.
Activate Assimilation Aegis' equip ability by paying {2}, attaching it to any other creature you control except Brass Squire.
Assimilation Aegis' second ability triggers, causing the creature to become a copy of Medomai the Ageless.
Repeat.

Infinite turns

Medomai the Ageless

Assimilation Aegis

Brass Squire

Declare any other creature as an attacker.
Holding priority, activate Brass Squire by tapping it, attaching Dinosaur Headdress to the attacking creature, and causing the creature to become a copy of Medomai the Ageless.
Deal combat damage using the creature.
The creature triggers, causing you to take an extra turn after this one.
Move to your postcombat main phase.
Activate Dinosaur Headdress' equip ability by paying {2}, attaching it to Brass Squire.
Repeat each turn.

Combos with "Brass Squire"