It already exists in the form of solo deep dungeon and Bozja duels. But there are two significant problems:
Solo deep dungeon is way too hardcore for the majority of players. HoH solo took me around 40 hours which is the same amount of time you'd dedicate to an entire Savage tier. There is no incentive for players to solo deep dungeons up to any point other than the top floor, which IMO is an extremely bad implementation.
Solution:
The new deep dungeon should remain extremely tough for those who want to solo up to the max floor. However, there needs to be significant rewards every 10 levels beyond a certain "hard" floor so that players can actually feel good about soloing them without feeling like it's a drag.
I think the new deep dungeon needs to have 150 floors. It should start getting as hard as HoH floors 50-60 at floor 80. Then allow people to choose between three starting points: 1, 41, and 81.
IMO, for rewards:
Reaching floor 90: a title and an exclusive minion (one-time). Difficulty: HoH 61-70, PotD 151-170.
Reaching floor 100: 360 weekly tomes (weekly reset) Difficulty: Hoh 71-80, PotD 171-189.
Reaching floor 110: an exclusive mount and glamour (one-time) Difficulty: HoH 71-80, PotD 171-189.
Reaching floor 120: a title and a one-time significant boost to relic weapon completion of your choice (e.g. skip the Harrowing Memory step) Difficulty: HoH 81-100, PotD 190-200.
Reaching floor 130: 20M gil (one-time) and 24 Savage books of your choice (one-time). One relic step completion of your choice (weekly reset). HoH 81-100, PotD 190-200.
Reaching floor 140: An exclusive mount and glamour (one-time). 3M gil (weekly reset). Harder than HoH/PotD.
Reaching floor 150: An exclusive title and two relic weapon step completions of your choice (one-time). One relic weapon step completion of your choice (weekly reset). Harder than HoH/Potad.
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Party mode rewards:
Floor 120: Title and one-time relic step completion.
Floor 150: Mount, 20M gil, glamours, and one-time relic step completion.
They do different things:
Floor 1 is for everyone to experience the new deep dungeon for the first time at a casual pace.
Floor 41 is for people who want to grind levels or other stuff.
Floor 81 is for the challenge mode and I hope that they enable achievements even if you start from Floor 81. At the moment HoH solo is a drag all the way until Floor 61, which is just a huge waste of time. I didn't even bother with PotD solo because I had to grind so many potions and grind through 150 floors of boring snoozefests. This needs to change. Make all floors starting from 81 challenging and engaging. This way you have 70 floors of challenging content.
This is the reward structure that I think should be used.
Also please make it a non-reskin deep dungeon. I don't think I will even touch it if it's just PotD reskin 3.0