It's an FGO crossover with A Certain Magical Index. Plot is basically Solomon send one of his Grails to Academy City, or Alister somehow stole one from across dimensions (would not be impossible for him) so it became a Singularity. Solomon and Allister are basically at war with each other, and so far three Demon Pillars have shown up.
I'm surprised no one posted before me, but it may be due to it being Christmas... but the Fate/Stay Night and Campione crossover of 'God Slaying Blade Works' by Marcus Galen Sands finally updated with chapter 46.
Personally, I'm not too keen on the chapter, but I'm glad the story is updating again.
I agree that was the low point of the fic... well, until this latest fiasco started as that was when he started slowing his releases by a lot.
However, there were a lot of interesting arcs after that... Tiamet and Gwenivere moving in... the vacation to an island, Tiamets new pet, the accountant getting stomped on, and living to tell the tale, the two girls from the history compilation committee repairing damage to Emiyas house and fixing the defenses, a trip to england, the hunting down of a rogue devil king and getting good blackmail material on him, and Gwenivere becoming his handmaiden.... curing of mother of Kaide, the culmination of Homuras plans, and we must not forget... Lancelot in a gaming/anime store....
So apparently there are Japanese fanfics for Fate Stay Night and other media. たとえ全てを忘れても - ハーメルン -- Amnesiac Shirou in Danmachi-verse. Highly recommended. 錬鉄の英雄 プリズマ☆シロウ - ハーメルン -- Prisma!Shirou picks up Archer's card somewhere in his house. 絶対魔獣戦線バビロニア - ハーメルン -- Humanity has burned and it's up to Chaldea to save the world but screw that (hasn't started their Babylon quest-line yet. They will in a couple of chapters from the looks of it). Let's focus on Post-UBW Rin and Shirou in Babylon. FGO fic. Tohsaka meets Tohsaka. Comedy for now. Why is this Gilgamesh so friendly?
If story of the Caster and Shirou meet https://syosetu.org/novel/132655/ The author also included bad ends in the story.