The first Tower Quest type event seems to have started on DMM yesterday. It seems to be one of those limited attempt type events (like Guild Order), and it's currently running alongside a guild order and a raid.

The basic idea seems to be you're trying to clear floors of a tower with specific restrictions. Clear the quest once, clear the quest with so and so number of kamihime alive, clear the quest with so and so element kamihime, clear the quest with so and so type of kamihime, etc etc.
All quests also have an additional condition: kamihime used in the event can't be used again in this event until 3 daily maintenances have passed. (and this one is running for ~8 days)

What's the point of this? You're getting tower medals from these. Tower medals can be exchanged for stuff (new exchange in the shop). You will also be ranked based on how many medals you gained. Yes, it's another competition against fellow players. The ranking prizes for this is tower medals (yep, even more) and jewels.

What kind of stuff can tower medals be exchanged for? They're mostly sets of stuff. For example, the most expensive set by far would be a pack of 1 SSR weapon limit break item, plus 2 of both types of grimoires. Then there's a bunch of packs which include 1 SSR accessory each and... rosaries? I'm not sure what the rosaries are for. A cheaper pack of just grimoires (5 of both types). A gacha ticket set (1 SR, 2 kamihime weapon, 5 plain). Skill enhancement grail set. 300 jewel pack. Different elemental fang/rune/bone/star packs. 1 SR weapon + 1 SR eidolon enhancement pack. 10k gems. 2 half-elixirs + 5 seeds. 30 soul points + 10 holy soul points.

Speaking of new exchanges in the shop, it seems that on November 29, another one was added. The Orichalcum exchange! Because apparently people have spare orichalcum by now. The only item I see listed in that exchange is... the SSR hammer from Jormungandr's event for 2 ori each!