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.
A really interesting storyline could be a time - travel one. Supergirl and Green Arrow are sent back in time to prevent a major event that would change the future of their worlds. They have to adapt to the past's technology and social norms while also trying to figure out who is behind the time - travel plot.
Perhaps a fanfiction where Supergirl and Green Arrow are transported to an alternate dimension. In this dimension, they have to rely on each other completely to find a way back home. Along the way, they discover secrets about each other's pasts that they never knew before, which deepens their bond.
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.
Supergirl is very much about truth and justice in a big - picture way. Green Arrow focuses on the justice that needs to be served on the streets. Their personalities could clash when they first meet as they might not understand each other's motives fully. However, as the story progresses, they can start to see how their different views on justice can work together. Supergirl can use her powers to help Green Arrow with larger threats that he couldn't handle alone, and Green Arrow can show Supergirl the importance of the little things in protecting a city.
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.
Kara Danvers (Supergirl) is also very popular. Her superpowers and kind - hearted nature make her a central figure. Fans love to see her interact with the more grounded characters from Arrow, like when she tries to understand their more human problems despite her god - like powers.
One interesting crossover could be the characters teaming up to fight a common supervillain. For example, Lex Luthor from Supergirl's world could team up with some of Arrow's villains like Deathstroke, and Team Arrow and Supergirl would have to combine their skills to take them down.
Another great storyline could involve a cross - dimensional rift that brings characters from Arrow's world into Supergirl's and vice versa. This would create a lot of chaos as the characters have to adapt to the different rules and environments. For example, Oliver might struggle with the presence of aliens in Supergirl's world, while Kara has to deal with the more gritty and crime - ridden Star City. It could also lead to some interesting character pair - ups and new friendships or rivalries.
In some fanfictions, there could be a storyline where the Flash and Arrow are transported to an alternate dimension. In this new world, they have to find their way back home while also dealing with the threats in that dimension. It could involve them meeting alternate versions of themselves or their friends, which would be really cool to explore.
There are some writers on popular fanfiction platforms like Archive of Our Own. A writer by the name of 'DC_Crossover_Pro' often writes amazing crossovers including Green Arrow and Batman. They have a unique style of writing that really delves into the personalities of the characters. Also, look for writers who have received a lot of positive reviews and feedback on their Green Arrow meets Batman fanfictions. Writers who are able to balance the different tones of the two heroes - Green Arrow's more light - hearted and quippy nature with Batman's dark and brooding one - tend to be the best at this kind of fanfiction.
One popular storyline is where Flash and Supergirl team up to fight a common, powerful enemy like a super - villain from another dimension. They combine their speed and strength in unique ways to save the world. Another is a more character - driven plot where they develop a romantic relationship. Flash's quick - witted charm and Supergirl's strong - willed nature make for an interesting dynamic. There are also storylines where they swap powers temporarily, leading to humorous and action - packed situations as they learn to use each other's abilities.
Lex Luthor would be a great choice. He could be causing trouble in Gotham as well as Metropolis. His intelligence and resources would pose a significant threat to both Supergirl and Batman. He might be trying to manipulate events to make the two heroes fight each other so he can carry out his evil plans.