Type-Moon from the Start, but a Magical Index Mage

Morpheus had transmigrated into the world of A Certain Magical Index and was still cleaning up the mess left behind by an evil magical society when he was swept into a temporal vortex and transported to the Type-Moon world. Reborn as a baby, he became the adopted son of House McRemitz and Bazett's younger brother. As he prepared for the Fifth Holy Grail War, he discovered that this was actually the world of FGO, where no such war existed. Thus, for the sake of world peace and to pursue the ultimate secret of magic once more, Morpheus Fraga McRemitz set out on the path to saving humanity as a Golden Mage, striving to become a Demon God.

...The blurb's not great. Harem, infinite worlds. FGO and Demon Slayer arcs complete. Currently in Overlord. Other worlds are still being considered.