Unfortunately, this dungeon hardlocks players out of proceeding further to title grind; the backside of the boss door leads back to the boss room, and no other exit from the boss room exists, so after beating the boss, you must immediately end the dungeon.
You can just reenter the dungeon afterwards though by interacting with the soul gem, in case you want those titles.
I'll also make dungeon 14 a little harder, and the boss of 13 somewhat easier.
Quick follow up, having gone back into Dungeon 14 as suggested...
The fact that all Amputation/Piercing progress is removed on reset made it a little more difficult to get the title; I was able to clear every mob in the dungeon from start to finish without using any limb-restoring item, or any girl losing all her limbs. In the process of clearing the dungeon, I found out that this is the place where the Revives were hidden! I've wanted these for a long time... but unless I missed something earlier, this is the first place where they've appeared. Certainly better late than never! I'd have been quite happy with an item that merely brought girls up from 0 to 1 HP, and these include full HP restoration for free, which is quite good. On the subject of healing items, I will note that the distribution of healing power is kind of weird, given health values; I've got 4 Red Liquids that heal 500 HP, 7 Orange Liquids that heal 200 HP... and Mami, my highest-HP girl, only has 151 HP. I don't really need potions quite this powerful... but the plentiful full heals do come in handy when I'm doing higher-attrition things.
Having made it to the boss with a completely pierced and limbless party, I decided to see if it was possible to beat the boss with the maximum handicap. The answer was yes... but it relied on quite a bit of luck, since if Madoka got chained up or knocked out, that's the fight. It took five tries for team nugget to beat the boss, but it was just barely possible. In hindsight, that's a challenge that would've been slightly easier if I'd ground to the level cap before trying it, but I was out of healing items, and didn't want to have to restart and regrind amputation to try for it. With the boss cleared a second time, I returned to the dungeon a third time to grind to cap... which took much less time than any of the rest of that, since the mobs here aren't especially dangerous to an able-bodied team.
