Triumphant Adventurer

Deathtouch
During your turn, this creature has first strike.
Whenever this creature attacks, venture into the dungeon. (Enter the first room or advance to the next room.)

Thorough Investigation

Whenever you attack, investigate. (Create a Clue token. It's an artifact with "{2}, Sacrifice this token: Draw a card.")
Whenever you sacrifice a Clue, venture into the dungeon. (Enter the first room or advance to the next room.)

The Council of Four

Whenever a player draws their second card during their turn, you draw a card.
Whenever a player casts their second spell during their turn, you create a 2/2 white Knight creature token.

Hama Pashar, Ruin Seeker

Room abilities of dungeons you own trigger an additional time.

Sefris of the Hidden Ways

Whenever one or more creature cards are put into your graveyard from anywhere, venture into the dungeon. This ability triggers only once each turn. (To venture into the dungeon, enter the first room or advance to the next room.)
Create Undead — Whenever you complete a dungeon, return target creature card from your graveyard to the battlefield.

Rilsa Rael, Kingpin

Deathtouch
When Rilsa Rael enters, you take the initiative.
Whenever you attack, target attacking creature gains deathtouch until end of turn. If you've completed a dungeon, that creature also gets +5/+0 and gains first strike and menace until end of turn.

Safana, Calimport Cutthroat

Menace
At the beginning of your end step, if you have the initiative, create a Treasure token. Create three of those tokens instead if you've completed a dungeon.
Choose a Background (You can have a Background as a second commander.)

Midnight Pathlighter

Creatures you control can't be blocked except by legendary creatures.
Whenever one or more creatures you control deal combat damage to a player, venture into the dungeon. (Enter the first room or advance to the next room.)