One possible storyline could be that Batman has to use his detective skills to find out a hidden threat to Superman before saving him. Maybe there's a kryptonite - based weapon that only Batman can detect and disable.
One interesting storyline could be a team - up against a powerful new villain that neither can defeat alone. They have to combine their unique skills, like Superman's super strength and Batman's detective skills.
In some Mpreg fanfictions, there could be a storyline where Batman and Superman have to figure out the genetics of their unborn child. Given their different origins - one being a Kryptonian and the other a human with no super - powers originally - it would be fascinating to see how their child might inherit or combine their abilities. There could also be a plot where they have to deal with time - traveling villains who try to prevent the birth of their child for some evil purpose.
A cool story could be about them having a friendly competition to see who can solve a series of mysterious crimes in the other's city first. Along the way, they learn more about each other's methods and develop a deeper respect for one another. This also gives an opportunity to explore the different atmospheres and challenges of Gotham and Metropolis.
One interesting storyline could be a young Superman and Batman teaming up for the first time in a kid - friendly adventure. Maybe they are trying to stop a group of small - time villains who are stealing toys from all the kids in Gotham. They use their unique powers and detective skills respectively to track down the bad guys and return the toys.
Lex Luthor is often a main antagonist. He might be the one who sets up the situation where Superman needs to be saved, like creating a powerful weapon or a devious plan to weaken Superman.
One interesting storyline could be them teaming up against a new supervillain that neither can defeat alone. They combine their unique skills, Superman's super strength and flight with Batman's detective skills and gadgets.
One interesting storyline could be a redemption arc for Superman. In the Injustice universe, Superman has gone down a dark path. A fanfiction might explore how Batman tries to bring back the good in him, with lots of emotional confrontations and moral debates between the two.
One interesting Batman Superman fanfic could be about them teaming up to face a new, extremely powerful villain that neither could defeat alone. For example, a villain with the power to manipulate time. In the story, Batman's strategic mind and Superman's superpowers combine in unique ways to outwit the foe.
One possible storyline could be Harley trying to reform and Batman being skeptical at first. For example, Harley could start doing small good deeds in Gotham, like helping out at an orphanage. Batman would be watching her closely, waiting for her to slip back into her old ways. Another idea is a story where Harley has some information that could help Batman take down a major villain, but she wants something in return, like a chance at a new life outside of Arkham Asylum.
One interesting storyline could be a team - up against a new super - villain who has the power to manipulate time. Batman and Batwoman would have to race against the clock to stop this villain before he changes history to his advantage.