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.
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 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.
In a 'Team Flash meets Supergirl' fanfiction, there could be an epic team - up. The Flash might use his super speed to save Supergirl from a kryptonite - powered trap. Then they could join forces to fight a common enemy like Lex Luthor or an alien invasion. The scientific minds in Team Flash could also help Supergirl understand some new aspects of her powers.
A great storyline could be about a mystery that spans both their cities. They start investigating separately but soon realize they need each other's help. Team Arrow has the skills to infiltrate dangerous locations, while Team Flash can quickly travel between the two cities to gather information. There could also be a storyline where a powerful and ancient artifact is discovered, and both teams want to keep it safe from falling into the wrong hands. They would need to overcome their differences in approach to protect the artifact and the world from its potential misuse.
In fanfiction, when Team Flash meets Team Arrow, there could be an exchange of superpowers knowledge. The Flash's speedster abilities might amaze the members of Team Arrow, while the archery and combat skills of Team Arrow could be something new for Team Flash to learn from. Maybe they would team up to fight a common and extremely powerful villain that neither team could handle alone.
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.
Well, Supergirl is used to being a solo hero or working with Superman. But with the Young Justice team, she'd bring in her Kryptonian strength and knowledge. The team members of Young Justice would be in awe of her powers at first. But they also have their own unique skills. For example, Robin is a great detective. He could help Supergirl in figuring out the motives of villains more quickly. Superboy, being a clone of Superman, might have an interesting relationship with Supergirl. They could compare their experiences of being related to Superman in different ways. Aqualad's leadership skills could also play a role in making sure Supergirl fits into the team's strategies well.
Supergirl would be really interesting. Her alien origin and her super strength, along with her ability to fly, would make her stand out. She could bring a new dynamic to Team Flash with her different set of powers and her more idealistic view of heroism, which might contrast with some of the more street - level concerns of Team Flash.
Love and romance can be a theme in some cases, not necessarily between Arrow and Supergirl directly, but perhaps within their respective teams or with other characters they interact with in the fanfiction world. It adds an extra layer of complexity to the relationships and the overall story.