A great plot could be that there's a threat to Metropolis and Gotham at the same time. Superman is more used to dealing with large - scale threats in Metropolis, while Batman is focused on the more shadowy, street - level crime in Gotham. But this time, the threats are intertwined. They need to combine their skills, Superman's super strength and flight with Batman's detective skills and strategic mind, to save both cities. Along the way, they could also have some friendly competitions about who can solve parts of the mystery faster.
Maybe in the fanfiction, Superman and Batman find out they have a common enemy from another dimension. They have to learn about the strange new powers and rules of this dimension to defeat the foe. They start off distrusting each other but as they face more and more difficulties, they begin to understand and respect one another better.
One idea could be that Superman and Batman have to team up to stop a new supervillain who has the power to manipulate time. This would force them to put aside their differences and work together in a really challenging situation.