I also have the following variant rule suggestions:
MINORITY OPINION
Items are generally worth what they are worth (they might be mass produced, belong to a famous person, are made of precious metals, etc.) but for some their value could be different (maybe they hate the famous person and don't want their stuff or this is a long lost family heirloom.) This means adventurers might want other classes' stuff, adding more dynamics to item exchange.
When making loot in step 3, add the following 2 rolls for both items:
Determine who among the party has a different opinion about this item (this can be you). This is easiest to do with a d12 or a d10 (for 5 players.) Alternatively you can roll d6/2 for 3 players, d20/5 for 4 players, d20/4 for 5 players or d6 for 6 players.
Determine what they think of the item, by rolling a d10 (0 means 0) or a d20/2 rounded down (1 and 20 are both 0.)
When introducing the item, ask the Player whose adventurer has the special opinion to explain why the item is special for them. If the item is carried by this adventurer, it counts as having this much Emotion, for everyone else- the normal amount.
EVIL PARTIES
Some players might be tired of Epic Fantasy with it's Noble Hero Adventurers and Black and White Morality (like Lord of the Rings), and instead like to play out a Dark Fantasy, where adventurers are Self-Serving Anti-heroes and morality is a grey mess (like Game of Thrones.) This variant is for them. (make sure all players are on board with this, because it will make the light-hearted comedic tone of GonParis much darker!) This should affect the description of the dungeon and party dynamics.
Add the following 4 phases:
Ostracism (aka Pride): at the end of Step 4, the party votes (by raising their hands of the count of 3, or by other means) on if they want to leave the least useful adventurer behind. If more than half raised their hands, the adventurer is Left Behind and the voting continues with the new least useful adventurer. Otherwise the phase is over.
Revenge (aka Envy): After all Failures in Step 5 are countered, the Left Behind adventurers roll a d20 against their peronsal total usefulness. Any who fail must describe how lacking an item (that was taken by another player or not take at all) has led to their demise (or getting lost in the dungeon forever.) Those who succeed move to the next phase...
Showdown (aka Wrath): for each Left Behind player that survived Revenge add another failure for the party. Determine if the party succeeds or fails. Go around the table describing how players use their items to fight the other group, players who haven't spoken yet is Step 5 (and the Left Behind) must contribute, the others may skip or join in at their own discretion. The result of the fight must match what was determined. If the party is defeated, the Left Behind (only the ones who survived Revenge and participated in Showdown) repeat steps 4 and 5 adding the defeated party's loot to their own. (Skip Ostracism this time.)
Betrayal (aka Greed): At the beginning of Step 6, just as the adventurers are about to go their separate ways, players have until the count of 3 to declare they are betraying someone. If they do, both they and their target roll d20 if they succeed (roll at or below their own Total Usefulness,) they have survived, but are winded, lightly wounded or just used up a resource- lower their usefulness by 1 until the end of Betrayal phase. If they fail (roll above Total Usefulness) they are killed, gravely wounded, knocked out or otherwise won't make it. Describe the fight. (If both players fail, they both don't make it, if both succeed - they can decide if they want to continue the fight or not.) After the fight, the rest of adventurers get to take any of the defeated player's stuff, with the winner (if there was one) getting first pick and the rest dividing what's left. Adventurers must discard items down to their maximum encumbrance, but once they do, can not continue discarding. Players may now betray again (note that Total Usefulness is not restored.)
(There are sadly no Lust, Gluttony or Sloth phases)