I chose Muldrotha, the Gravetide as the Commander for not only the color wedge, but the guaranteed recursion for all permanent types is extremely useful in this deck. You don't need Muldrotha, the Gravetide on the field for this deck to function, it just is a nice assist. Other good Commander alternatives are Jarad, Golgari Lich Lord and Marrow-Gnawer. You will lose blue in both of these Commanders, but they can function similarly to this deck. Marrow-Gnawer can be very successful in mono black but you will lose access to some fantastic synergy in Green.
When brewing a Rat EDH deck, you choose to either go with Rat Colony or Relentless Rats.
Both allow you to run as many as you want within the deck, however I chose Rat Colony over Relentless Rats for a few reasons:
1) Colony gets +1/+0 for all other rats, while Relentless Rats only benefits from other Relentless Rats. This has synergy with Marrow-Gnawer to pump your Rat Colony by making more rats, as well as Ogre Slumlord who will make more rats whenever a nontoken creature that you control dies. Additionally this power boost from all rats has synergy with Greater Good and Altar of Dementia
2) You can Skull Clamp them.
3) They are cheaper, as Relentless Rats cost 3 CMC.
Why only 18 Rat Colony? People seem to run 25-30 (sometimes more) when brewing a rat deck like this. I decided to run 18, as just under a 5th of the deck is still Rat Colony, but it is less likely to create scenarios where all I'm drawing is rats over and over again. You want rats in hand or graveyard, but you need to pull other cards than just rats and lands.
Now that you agree Rat Colony is the superior unlimited rat choice, let's get to the deck.
What set me down this rat path was two cards: Bloodbond March and Secret Salvage. These are your power cards, they get the deck really going.
Bloodbond March will cause all of your Rat Colony to return from the graveyard to play when a Rat Colony is played. That means you can put out these rats from anywhere and all rats of the same name will then proceed to fill the battlefield from the graveyard. The result of this can cause multiple loops of all 18 Rat Colony to move in and out of the graveyard. This synergies amazingly with Greater Good, Altar of Dementia, Kindred Discovery and the most important Syr Konrad, the Grim.
Secret Salvage is your "give me every single Rat Colony in my deck right now" tutor. As long as one Rat Colony is in your graveyard, you can pull the other 19 out of your deck and right into your hand. Now, other than the obvious "get me all my rats," this can be synergize with some other cards we are running. First off with all these rats in your hand, might as well use it to tutor more. Insidious Dreams will allow you to discard any number of cards to stack your library with. Might as well discard 3-5 rats and get the pieces you need. Syr Konrad, the Grim will ping your opponents for each Rat Colony discarded. Pulling all your rats out of your library and into your graveyard also fuels Bloodbond March in the process.
Titans' Nest is a fantastic card with this Commander. Basically it allows you to surveil on every upkeep, and every colored spell in your deck now as delve (with the exception of x spells). Drawing off your rat syngeries will allow you to delve out unneeded cards in the graveyard and basically add colorless mana for nothing. I can't recommend this enough for not only this deck, but any graveyard deck with Sultai colors.
Other than just straight up rat attacks (with aid of Concordant Crossroads, Tetsuko Umezawa, Fugitive, and/or Coat of Arms), Syr Konrad, the Grim is the wincon. The repeated dumping of as many rats as possible in and out of the graveyard will damage all your opponents consistently. If Syr Konrad, the Grim dies, just bring him out with Muldrotha, the Gravetideonce more.
This deck is weak on interaction, really only having Damnation and Attrition as a means to remove opponents creatures, but it is a deck focused on utilizing the above mentioned cards to win via a swarm of rats. I have a great time with this deck and hope you can enjoy it as well.
I left some good alternatives in the Maybe Board, as they were cards I considered or removed while brewing this deck.
