Place a gremlin shaman beside Punch and Vise in the Bazaar.
S/He grants you an item that increases the chance of a specific variant on one Unique Variant at one Ticket Roll.
(CTR & ASI NOT INCLUDED, that's broken)
This item doesn't have a 100% chance, you have to upgrade it for that to happen.

Acquirement + means of upgrading?
1) Monster- & status-themed materials

For example, Blaze Pepper drops from fire-themed enemies => required material for a fire resistance chance-up item
Royal Skewer is dropped from slimes only => required material for a damage bonus against slime chance-up item

2) A new kind of mechanic that involves the treasure rooms at the end of each danger prestige mission. (and/or shadow lairs maybe?)
Instead of only one group button leading to the treasures above, there's a new way going down.

Not sure if there will be another challenge in order to get that specific item OR if it will be a one-or-the-other choice.

Anyway, in order to restrict the item so that you can't just leave and start anew after you get that item and before you reach the lift, the item will be a little bit special. Let's call it -soul-.
You need an object that's purchasable from the gremlin shaman. It's needed to collect a soul and it is restricted like this:
- It's restricted to one buyable copy a day
- You can only gather one soul at a time
- If you gather it on a danger prestige mission, you'll have to enter the lift in order to -seal- it. Similarly to minerals!
- Doesn't matter if there's a soul in it or not - after the day changes it will cease to exist, so you have to gather it and craft the chance-up item on the same day

Compound 42 drops Fire-, Poison-, Gremlin- and Slime-Souls
Ghost in the Machine drops Shock-, Construct- and Undead-Souls
Heart of Ice drops Freeze-, Beast- and Fiend-Souls.
Legion of Almire drops Curse-, Stun- and Undead-Souls (not sure about the curse, but the almirian guards can afflict that status)

(We need a danger prestige missions with Sleep-Status (maybe curse, too).)

The gatherable souls per mission are a random amount between 0-2. (So you can choose, remember: only one soul once per day)
Souls have star-grades, that's influenced by luck and the difficulty you played the danger mission with.

The grade of the soul should play a role in upgrading the chance-up item somehow.

>>> The upgrading only increases the chance of that specific UV to appear, the actual grade (Low, Medium, High, Very High, Ultra, Maximum) is still entirely RNG-based! <<<

And the most important point of it all: Everything is BOUND, you have to move your a** all by yourself.
The only sellable things are the materials.

I hope this gives materials more importance, it also could make danger prestige missions more of a big deal rather than, well, just Prestige and 0-12 Radiant Fire Crystals.
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Free to discuss, this idea is entirely made-up on the spot after waking up. (o>o)-cU