The Initiative

Whenever one or more creatures a player controls deal combat damage to you, that player takes the initiative.
Whenever you take the initiative and at the beginning of your upkeep, venture into Undercity. (If you're in a dungeon, advance to the next room. If you're not, enter Undercity. You can take the initiative even if you already have it.)

Undercity

You can't enter this dungeon unless you "venture into Undercity."
Secret Entrance — Search your library for a basic land card, reveal it, put it into your hand, then shuffle. (Leads to: Forge, Lost Well)
Forge — Put two +1/+1 counters on target creature. (Leads to: Trap!, Arena)
Lost Well — Scry 2. (Leads to: Arena, Stash)
Trap! — Target player loses 5 life. (Leads to: Archives)
Arena — Goad target creature. (Leads to: Archives, Catacombs)
Stash — Create a Treasure token. (Leads to: Catacombs)
Archives — Draw a card. (Leads to: Throne of the Dead Three)
Catacombs — Create a 4/1 black Skeleton creature token with menace. (Leads to: Throne of the Dead Three)
Throne of the Dead Three — Reveal the top ten cards of your library. Put a creature card from among them onto the battlefield with three +1/+1 counters on it. It gains hexproof until your next turn. Then shuffle.

Undercity // The Initiative

Hama Pashar, Ruin Seeker

Room abilities of dungeons you own trigger an additional time.

Lost Mine of Phandelver

Cave Entrance — Scry 1. (Leads to: Goblin Lair, Mine Tunnels)
Goblin Lair — Create a 1/1 red Goblin creature token. (Leads to: Storeroom, Dark Pool)
Mine Tunnels — Create a Treasure token. (Leads to: Dark Pool, Fungi Cavern)
Storeroom — Put a +1/+1 counter on target creature. (Leads to: Temple of Dumathoin)
Dark Pool — Each opponent loses 1 life and you gain 1 life. (Leads to: Temple of Dumathoin)
Fungi Cavern — Target creature gets -4/-0 until your next turn. (Leads to: Temple of Dumathoin)
Temple of Dumathoin — Draw a card.

Tomb of Horrors Adventurer

When this creature enters, you take the initiative.
Whenever you cast your second spell each turn, copy it. If you've completed a dungeon, copy that spell twice instead. You may choose new targets for the copies. (A copy of a permanent spell becomes a token.)

Dungeon of the Mad Mage

Yawning Portal — You gain 1 life. (Leads to: Dungeon Level)
Dungeon Level — Scry 1. (Leads to: Goblin Bazaar, Twisted Caverns)
Goblin Bazaar — Create a Treasure token. (Leads to: Lost Level)
Twisted Caverns — Target creature can't attack until your next turn. (Leads to: Lost Level)
Lost Level — Scry 2. (Leads to: Runestone Caverns, Muiral's Graveyard)
Runestone Caverns — Exile the top two cards of your library. You may play them. (Leads to: Deep Mines)
Muiral's Graveyard — Create two 1/1 black Skeleton creature tokens. (Leads to: Deep Mines)
Deep Mines — Scry 3. (Leads to: Mad Wizard's Lair)
Mad Wizard's Lair — Draw three cards and reveal them. You may cast one of them without paying its mana cost.

Dungeon Delver

Commander creatures you own have "Room abilities of dungeons you own trigger an additional time."

Radiant Solar

Flying, lifelink
Whenever this creature or another nontoken creature you control enters, venture into the dungeon. (Enter the first room or advance to the next room.)
{W}, Discard this card: Venture into the dungeon and you gain 3 life.

Tomb of Annihilation

Trapped Entry — Each player loses 1 life. (Leads to: Veils of Fear, Oubliette)
Veils of Fear — Each player loses 2 life unless they discard a card. (Leads to: Sandfall Cell)
Sandfall Cell — Each player loses 2 life unless they sacrifice a creature, artifact, or land of their choice. (Leads to: Cradle of the Death God)
Oubliette — Discard a card and sacrifice a creature, an artifact, and a land. (Leads to: Cradle of the Death God)
Cradle of the Death God — Create The Atropal, a legendary 4/4 black God Horror creature token with deathtouch.

Eccentric Apprentice

Flying
When this creature enters, venture into the dungeon. (Enter the first room or advance to the next room.)
At the beginning of combat on your turn, if you've completed a dungeon, up to one target creature becomes a Bird with base power and toughness 1/1 and flying until end of turn.

Nadaar, Selfless Paladin

Vigilance
Whenever Nadaar enters or attacks, venture into the dungeon. (Enter the first room or advance to the next room.)
Other creatures you control get +1/+1 as long as you've completed a dungeon.

White Plume Adventurer

When this creature enters, you take the initiative.
At the beginning of each opponent's upkeep, untap a creature you control. If you've completed a dungeon, untap all creatures you control instead.