Overlord X Fate Crossover
What if Ainz chose to play as a vampire Magic-user in Yggdrasil, and when the game supposed to shut down he later awakens on the moon as a True Ancestor. With the information that he is a replacement of the Brunestud.
Those who play FGO know this, but True Ancestors are extinct in Fate Timeline due to the great conflict between the 2 factions. Arcueid hinted to be the sole survivor, but she seems to have been asleep.
Ainz tasked to save Gaia by the moon, Ainz himself also didn't against the idea as he comes from the timeline where humanity ruined the planet. You guys can later choose, whether Ainz gonna be trigger happy murdering people or probably learn about the world first.
You guys can choose the timeline yourselves:
Fate Zero: Ainz hangs out in Fuyuki looking at 21st Century Japan, until he saw Servant for the first time, and decides to observe the fight. it was only later after he learns about it's a prize that he gonna kill Kayneth and take his command seal. Making Diarmuid his Servant by forces. He will use Control Amnesia controlling Diarmuid mind to follow his order. Ainz biggest Challenge will be Gilgamesh, even after receiving a boost as True Ancestor, he will have trouble fighting Gilgamesh. So instead he will make use of Saber and manipulate her to fight Gilgamesh, and later kill him when Gilgamesh too distracted. He will later kill Diarmuid himself and won the war, but after finding out it just gonna twist his wish he destroys it himself.
Lord El-Melloi Case File: Ainz interested in this world Magecraft makes some money and enrolls in the clock tower pretending to be human using some item or spell. He will later see the whole politic inside the Clock Tower.
Fate Stay Night: Unlike in Fate Zero plot, Ainz learned that the Holy Grail is already tainted from the curse remain at the Fuyuki, so he has no interest in the Grail itself. Instead, he will be interested in the Servant itself, he will be interested with Noble Phantasm and when he found out Shirou has the ability to copy them. Oh, he will do everything he can to make Shirou his property.
Fate Hollow Atraxia: The Grail War is over but Angra Mainyu still remains trying to survive, Ainz took an interest in him and turn him into a Dead Apostle. Instead of creating a loop, it will be Ainz making use of Angra Mainyu.
Fate Apocrypha: In this story, Ainz makes an agreement with Kotomine Shirou, and agree to help him under the condition that they will fight as the final participant. It was pretty much guaranteed that Ainz will win if the sole participant remain is only Ainz and Kotomine, but Kotomine will have his own trick to out maneuver Ainz.
Fate Kaleid (Illya Timeline): Ainz took interest in Class Card, and try to rob it from Illya group. But this time Zelretch actually interfere as he like to avoid any chance Ainz finding out about Miyu origin.
Fate Kaleid (Miyu Timeline): Ainz saw Shirou fight to protect Miyu, at first he want to take advantage of Miyu but seeing Shirou fight so bravely he changed his mind. He decides to save Shirou out of a whim and try to enter the portal that opened through Shirou's wish for Miyu happiness while carrying Shirou with him.
Fate Extra: I have no idea how Ainz can exist in the world without Mana, and Moon Cell itself kinda contradicts the plot of Tsukihime. It kinda impossible, but up to you.
Fate Grand Order: Ainz arrived in the timeline after Solomon and Animusphere won their war, and both of them take their own path. Animusphere building Chaldea, and Romani is trying to live as a human in medical school. Ainz by chance meeting Romani, and while Romani has no power he immediately recognizes him as a True Ancestor. However, seeing Ainz has not much hostility toward human rights now he took risks and try to befriend the True Ancestor. Romani would be surprised at how reasonable Ainz is and his lack of will to outright kill humanity. They will keep in contact from time to time after that, and on the promised day, under Romani request, Ainz visited Chaldea. Ainz will then meet Fujimura/Gudako the sole Master left in the Chaldea and help him at the first fight.
Please choose whatever plot work for you