When you approach Mephisto and he is still peaceful, he does not demand tribute to pass like normal. Instead, he offers to buy your soul in exchange for powerful assistance on your quest to get the Amulet. If you agree, you are given amazing combat advantages (huge intrinsic damage boost, huge intrinsic AC boost, etc).

One of two bad things can happen as a result:

1. You have some chance, maybe 1/3, of failing to ascend when offering the Amulet to your god, as Mephisto claims your soul (the god still gets the Amulet but cannot raise you to immortality, so it’s a weird “win” that is not an ascension).
2. While ascending through Gehennom with the Amulet, he may reappear and try to take it and everything else for himself. All buffs he gave you are instantly removed and perhaps some debuffs are even applied. Possibly, defeating him in this circumstance could yield your soul back.

Alternatively he might appear on Astral, but that could be hard to explain flavor-wise. Or just create some test for if the player is in a sufficiently dire condition, and when they are he claims the player’s soul.

If you already have the Amulet the first time you meet Mephisto, he may not offer a bargain at all.