Activate Marrow-Gnawer by tapping it and sacrificing another Rat.
When the Rat dies, Marrow-Gnawer triggers, untapping itself.
Resolve the Marrow-Gnawer ability from step 1, creating a number of 1/1 Rat creature tokens equal to the number of Rats you control.
Repeat.

Infinite creature tokens

Infinite ETB

Infinite LTB

Infinite sacrifice triggers

Infinite death triggers

Marrow-Gnawer

Thornbite Staff

Activate Marrow-Gnawer by tapping it and sacrificing another Rat, creating at least two 1/1 Rat tokens.
Intruder Alarm triggers once for each creature token created, untapping all creatures that many times.
Repeat.

Infinite mana creatures you control can produce

Infinite untap of all creatures

Intruder Alarm

Activate Marrow-Gnawer by tapping it and sacrificing another Rat, creating at least three 1/1 Rat creature tokens.
Activate Ashnod's Altar twice by sacrificing two Rat tokens, adding {C}{C}{C}{C}.
Activate Sword of Paruns by paying {3}, untapping Marrow-Gnawer.
Repeat.

Infinite colorless mana

Infinite untap of creatures you control

Ashnod's Altar

Sword of the Paruns

Activate Marrow-Gnawer by tapping it and sacrificing another Rat.
When the Rat dies, Faces of the Past triggers, untapping all Rats.
Resolve the Marrow-Gnawer ability, creating a 1/1 Rat creature token for each Rat you control.
Repeat.

Faces of the Past

Activate Marrow-Gnawer by tapping it and sacrificing another creature, creating at least two 1/1 Rat creature tokens.
When the Rats enters the battlefield as a Pirate due to Maskwood Nexus, Coercive Recruiter triggers twice, untapping Marrow-Gnawer, and causing you to untap any other creature and gain control of it until end of turn.
Repeat.

Gain control of any number of creatures until end of turn

Coercive Recruiter

Maskwood Nexus

Activate Marrow-Gnawer by tapping it and sacrificing another Rat, creating at least one 1/1 Rat creature token.
When the Rat enters the battlefield as a Pirate due to Conspiracy, Coercive Recruiter triggers, untapping Marrow-Gnawer.
Repeat.
If you control at least two other Rats, this combo creates infinite additional Coercive Recruiter triggers, which can be used to untap any creature(s) infinitely and/or to gain control of any number of creature(s) until end of turn.

Conspiracy

Activate Marrow-Gnawer by tapping it and sacrificing another Rat, creating at least one 1/1 Rat creature token.
When the Rat enters the battlefield as a Pirate due to Arcane Adaptation, Coercive Recruiter triggers, untapping Marrow-Gnawer.
Repeat.
If you control at least two other Rats, this combo creates infinite additional Coercive Recruiter triggers, which can be used to untap any creature(s) infinitely and/or to gain control of any number of creature(s) until end of turn.

Arcane Adaptation

Activate Marrow-Gnawer by tapping it and sacrificing another Rat, creating at least one 1/1 Rat creature token.
When the Rat enters the battlefield as a Pirate due to Xenograft, Coercive Recruiter triggers, untapping Marrow-Gnawer.
Repeat.
If you control at least two other Rats, this combo creates infinite additional Coercive Recruiter triggers, which can be used to untap any creature(s) infinitely and/or to gain control of any number of creature(s) until end of turn.

Xenograft

Activate Robaran Mercenaries using Marrow-Gnawer's ability by sacrificing a Rat and tapping it, creating at least six 1/1 Rat creature tokens.
Activate Phyrexian Altar four times by sacrificing four Rats, adding {3}{B}.
Activate Robaran Mercenaries using Fain's fourth ability by paying {3}{B}, untapping Robaran Mercenaries.
Repeat.
Once you have infinite creature tokens, you may instead activate Fain's first ability to put infinite +1/+1 counters on creatures you control.

Combos with "Marrow-Gnawer"