Maybe a story where the Avengers are transported to Supergirl's universe. They have to adapt to her world's rules and help her fight against a powerful villain there. This could involve a lot of world - building and character development as the Avengers learn about Supergirl's allies and enemies.
Fanfiction.net is also a great place. There are many talented writers who create fanfics involving these characters. Browse through the categories related to superheroes, and you might stumble upon some amazing Avengers and Supergirl stories. However, the quality can vary, so be prepared to do some sifting.
Supergirl would probably start by introducing herself and her powers. The Avengers would likely be in awe of her abilities. They might ask her to join them on a mission right away. Supergirl could say yes and then start showing off her skills during the mission.
A really interesting plot could be a time - traveling crossover. Supergirl goes back in time to the era of the original Avengers. She helps them in a battle that changes the course of history. In return, the Avengers help her find a way back to her own universe. During this time, she forms a special bond with Thor, as they both have superhuman strength and a connection to otherworldly powers.
Well, she might show off her super strength and flight abilities to the Avengers. They could be both impressed and a bit wary at first. Maybe she'd team up with Thor and they'd have a friendly competition about who can fly faster or hit harder. Then she could also share her knowledge of different threats from her own universe with the Avengers, and together they could come up with new strategies to face common enemies.
Some of them would be in awe. For instance, Hawkeye would be amazed by Supergirl's powers. He might even joke about how his arrows seem useless compared to her abilities. Hulk might initially be aggressive, but if Supergirl showed she wasn't a threat, he could become curious. Iron Man would probably want to study her powers, maybe even try to incorporate some of her technology into his suit if possible.
Well, they might first be a bit suspicious of each other. The Avengers are used to their own world of threats and heroes, and Supergirl comes from a different universe in the DC world. Maybe Iron Man would be the first to start analyzing Supergirl's powers. He'd be really intrigued by her flight and super strength. Captain America, on the other hand, would probably be more focused on whether she could be trusted. And Supergirl would be equally curious about these new heroes. She might find Thor's hammer really interesting and wonder if she could lift it.
A 'Avengers Supergirl Crossover Fanfiction' might involve Supergirl's Kryptonian powers being a mystery to the Avengers at first. She could show off her super strength, heat vision, and flight, and the Avengers would be in awe. Then they'd start to strategize together. For example, Captain America would lead the group with his military tactics, while Supergirl uses her powers to do the heavy - hitting. And Hulk and Supergirl could have a fun interaction comparing their strength.
One could be a Supergirl fanfic about her teaming up with other superheroes from different universes to fight a powerful cosmic villain. It would involve epic battles and interesting character interactions.
One great 'Supergirl fanfic' is 'A New World for Supergirl'. It explores an alternate universe where Supergirl has different powers and faces new challenges. It's really interesting as it delves deep into her character development in a unique setting.