pukunui
Legend
So does the entrance to Undermountain.The known entrances show graffiti from generations of spelunkers.
Did you ignore the provided adventure hooks?With Dungeon of the Mad Mage, there isn't even anything clear about "should we explore deeper?" It's just nothing. No inspiration.
For the purely mercenary, there's the Chultan cleric lady who will pay in platinum coins for magic items and spellbooks recovered from Undermountain.
There are a number of quests that require the PCs to descend as far as the third floor (one of which involves visiting Skullport).
Someone is looking for a stolen gem that can be found on the tenth floor.
A City Watch captain wants the PCs to grab a piece of Halaster's Runestone from the twentieth floor.
There are also a variety of other quests that can be picked up as the adventurers explore. On the 3rd floor, there's a quest to retrieve the blind hobgoblin warlord's magical dagger that gives him blindsight. It was stolen by duergar who can be found on the 6th floor.
And so on.
Plenty of reasons to delve deeper!
For the second party in my campaign, I also used Halaster's Goal #1: Clean House. So I had him tell the PCs that if they could wipe out the drow in Undermountain and end the githyanki-mind flayer conflict, then make it down to his lair at the bottom, he'd reward them with a wish. This motivated them to go all the way.
I should add that I got rid of the level-limit on the magic portals. A few times the PCs portaled too deep. It made for some fun times!
If I were to run this again, I might try the game show option again and this time I would make it so Halaster seals off the exits behind the PCs so they can only ever go down. No going back up and no leaving the dungeon. It's a race to the bottom!