The best crossovers often explore the different power dynamics. Supergirl's super strength and flight compared to the Winchesters' hunting skills and knowledge of the occult make for an interesting mix. There are fanfictions where they exchange knowledge, like Supergirl learning about ancient spells from the Winchesters and the brothers getting tips on how to take down powerful foes from Supergirl.
One interesting plot could be that the Supergirl characters find themselves in the Supernatural universe. Maybe Kara has to deal with demons and angels while trying to find a way back to her own world. She could team up with Sam and Dean to fight a common enemy, like a powerful demon who has a vendetta against both the Supernatural world and Kryptonians.
On the other hand, Sam and Dean's knowledge of the supernatural would be invaluable to Supergirl. They could teach her about different types of demons, how to detect them, and what weaknesses they have. Their skills in using various weapons like the Colt or salt - loaded shotguns could be combined with Supergirl's powers. For instance, Dean could shoot a salt - loaded shotgun at a group of demons while Supergirl uses her super breath to blow the salt towards a wider area, maximizing the effect.
First, do your research on both shows. Know the characters, their backstories, and their powers. For Supernatural, understand the lore of demons, angels, and the hunting world. For Supergirl, learn about Krypton, her powers, and her relationships in National City.
One idea could be that a powerful villain threatens both their cities simultaneously. Supergirl and The Flash have to team up, and in the fanfiction, their different powers and personalities could lead to some interesting interactions. For example, Supergirl's strength and The Flash's speed could be combined in unique ways to defeat the villain.
One idea could be that Supergirl's powers are misinterpreted by Shield as a new threat. So they send some of their agents to investigate. The agents then realize she's actually a hero and they team up to fight a common enemy like a powerful alien race that's planning to invade both their worlds.
In this Naruto and Supergirl crossover, Naruto is on a mission in a strange new world and suddenly meets Supergirl. They initially misunderstand each other as threats. But as they start to communicate, they realize they both have a strong sense of justice. They team up to stop a powerful villain who is using a mix of ninja and Kryptonian technology to wreak havoc. Naruto uses his shadow clones and rasengan, while Supergirl uses her heat vision and super strength to take on the baddie.
First, you need to understand the characters well. For Supergirl, know her powers, her moral code, and her relationships. For Agents of Shield characters, like Coulson, Daisy, etc., study their personalities and abilities. Then, create a believable scenario for their meeting. It could be something like a shared threat or an accident that brings them together.
In a fanfiction scenario where Barry is stabbed during a Flash - Supergirl crossover, it could lead to a lot of interesting plot developments. Maybe Supergirl would have to step up and use her powers in new ways to protect Central City in Barry's absence. She might have to team up with the other members of Team Flash more closely.
One great Supergirl crossover fanfiction is 'Supergirl and the Flash: Worlds Collide'. It has an exciting plot where Supergirl and the Flash team up to face a common enemy that can manipulate time and space. The story does a great job of capturing the essence of both characters and their unique powers.