Another concept could be that Alex is an amnesiac who has a connection to one of Batman's old foes. Batman tries to help Alex regain his memories while also protecting him from the bad guys who are after Alex because of his potential knowledge.
One idea could be to explore what would happen if Alex Rider had to team up with a former enemy. Maybe they discover they have a common foe and must put aside their differences.
One idea could be a story where Batman has to team up with his rogues gallery to fight a greater threat from outer space. Maybe the Joker, Two - Face and the Riddler are forced to put aside their differences when an alien race starts to invade Gotham. They find that Batman's strategic mind and their own unique skills are needed to save the city.
One idea could be exploring Batman's early days as a vigilante in more detail. Show his first encounters with the major villains and how he developed his crime - fighting techniques.
One plot idea could be that Brittany and Alex are in a small town and they discover a hidden treasure map. They then embark on an adventure together, facing various challenges and growing closer as they search for the treasure. Along the way, they might have to outwit some local villains who also want the treasure.
One idea could be a story where Batgirl has to save Batman from a new and powerful villain. Maybe this villain has a special weapon that can neutralize Batman's skills, and Batgirl uses her unique abilities, like her gymnastic skills and her knowledge of technology, to turn the tables.
Another interesting fanfic could be set in an alternate universe. In this universe, Batman is a young rookie and Batgirl is his more experienced mentor. It would be a role - reversal story where Batgirl teaches Batman the ropes of fighting crime in Gotham. This could include her showing him how to use his gadgets more effectively and how to read the criminal underworld better.
A cool batman crossover fanfic idea might involve a crossover with the Avengers. Batman's strategic mind and detective abilities would be a great addition to the superhero team. He could help Iron Man with tech, or use his stealth to outwit Loki. Also, a crossover with the Doctor from Doctor Who could be fascinating. Batman could travel through time and space with the Doctor, solving mysteries in different eras.
Another story idea is that the Joker somehow gets his hands on a powerful and mischievous Pokemon like Ditto. Ditto can transform into any other Pokemon, and the Joker uses it to create all sorts of mayhem in Gotham. Batman has to figure out how to stop the Joker and his shape - shifting Pokemon while also dealing with other criminals who see this as an opportunity to cause more trouble.
A plot where Alex and Sara are stranded on a deserted planet together. They have to rely on each other's skills to survive. Sara's combat and survival skills from her time as a pirate, and Alex's scientific knowledge could make for an exciting story of cooperation and friendship. It could also explore a possible romantic relationship between them as they grow closer during their time of isolation.
One idea could be that Raven is in danger from a new dark magic threat and Batman, with his detective skills, helps her track down the source. They start to learn from each other, Raven about Batman's human tenacity and Batman about Raven's otherworldly powers.