A really cool story could be set in an alternate universe where Supergirl and Batman are the last two heroes left. They have to rely on each other completely and in the process, they discover new aspects of their powers and themselves. Their relationship could evolve from just being allies to something more complex and deep, with Supergirl teaching Batman to have more faith and Batman teaching Supergirl more about strategy.
One great storyline could be a villain that is causing chaos in both Arrow's Star City and Supergirl's National City. The two heroes team up, with Arrow using his combat skills and Supergirl using her superpowers to take on the baddie. They might initially have some differences in their approaches, but over time, they learn from each other and form a strong bond.
One common storyline is that they meet during a big crisis that requires both their skills. They start off as reluctant allies and gradually develop feelings. Another is where Supergirl, new to Earth, seeks Batman's help to understand the darker side of humanity, and they fall in love during this process.
Perhaps a fanfiction where Supergirl arrives in Smallville during a time when Clark is struggling with his identity. She could be a source of inspiration for him, showing him the full potential of his powers. They could also have a friendly competition to see who can save more people in Smallville, which would be a fun and exciting plot.
One common plotline is a team - up where Batman and Supergirl join forces to take on a powerful villain like Darkseid. They combine their different skills, Batman's strategic mind and Supergirl's super - strength and flight.
One great storyline could be them teaming up to fight a common enemy like a powerful meta - human who is causing chaos in both of their cities. They could start off not trusting each other fully due to their different methods but then grow to respect one another as they see the value in each other's skills.
Another interesting idea is a mind - control situation. A powerful telepath takes control of some of the heroes and villains in their respective cities. Flash, Arrow, and Supergirl have to find a way to break the mind - control. They start by finding the source of the telepath's power. Along the way, they discover that the telepath has a tragic past that led to this misuse of power. They try to reason with the telepath while also fighting off the controlled allies and villains.
One common storyline could be the little girl looking up to Supergirl as a role model. For example, the little girl might witness Supergirl saving the day and then be inspired to be brave in her own life, like standing up to bullies at school. Another could be Supergirl taking the little girl under her wing to protect her from some sort of danger that is targeting the girl because of her special abilities or knowledge. Maybe the little girl has a unique connection to an alien artifact and Supergirl has to keep her safe from those who would misuse it.
One popular storyline is them teaming up to fight a common enemy. Maybe a new super - villain that neither could defeat alone. This allows for a lot of action and showcases their individual powers well.
One idea could be that Batman and Supergirl team up to stop a powerful alien threat that is beyond the capabilities of either of them alone. They start off distrusting each other due to their different methods, but as they face challenges, they learn to work together and respect one another's skills.
One great storyline could be where Arrow and Batman team up to take on a common enemy like Ra's al Ghul. Arrow's skills with the bow and his street - level fighting ability combined with Batman's detective skills and high - tech gadgets would make for an exciting adventure. They could start off as rivals, not fully trusting each other, but as they face the challenges set by Ra's, they learn to work together and respect each other's methods.