Story Idea:
Batman and the entire Bat Family have to leave Gotham suddenly and unexpectedly unattended for an extended period of time because of... reasons. Maybe they have to go to space, that's usually where characters have gone for this sort of thing.
So, to cover for him while he's out, Batman has brought in... Spider-man, from the Marvel universe.
Why Spider-man? Bruce Wayne has money, Peter Parker needs money (even if it's from another dimension). And he's smart.
And I think during the entire run, it would be a hilarious running gag that Peter just has ZERO time for The Joker. Like, Joker escapes from Arkham and winds up hanging from the Crook Depository Hook outside Gotham PD in under an hour. No banter, no battle, not even shown in the comic. He just refuses to engage with the Joker at all, which drives the Joker even more insane.