Well, perhaps Captain America could be on a mission to seek an ancient Asgardian weapon to help in the fight against a new threat on Earth. He might meet Thor and the other Asgardians, and have to prove himself worthy in their eyes, just like he did in his own world.
Maybe he gets transported to Asgard by accident. Once there, he could be caught up in the political intrigue of Asgard. He might side with Loki in some unexpected situation, seeing a different side of Loki that no one else has. And then he has to find his way back to Earth while also dealing with Asgardian problems.
He could also meet Odin. Odin might view Captain America as an interesting mortal from Midgard and might have some words of wisdom or a task for him to complete during his stay in Asgard.
In this fanfic, perhaps there's a power struggle. Some power - hungry group on Earth wants to take over Asgard's resources or technology. They manipulate the situation to make it seem like Asgard is a danger, so Earth goes to war. Asgard, on the other hand, is just trying to protect itself and its way of life.
One possibility is that he wakes up and discovers new allies. The story could then revolve around him building relationships with these new characters while still holding onto his old values. He may also have to deal with the fact that the world has moved on without him and find his new place in it.
One possible plot could be Harry going to America to study at a new wizarding school. He might encounter new magical creatures and spells unique to the American wizarding world. He could also make new friends and enemies there.
He might be amazed by the grandeur of Asgard. Its golden palaces and powerful magic could both intrigue and intimidate him. Maybe he'd meet Thor and they'd exchange stories about their different kinds of magic and heroic deeds.
Well, perhaps a plot where they accidentally end up in an alternate dimension. In this dimension, their powers are different. Captain America might have some super - speed and Superman might have a more tactical mind like Cap. They have to figure out how to get back to their own dimension while also dealing with the villains of this new world. They learn from each other's skills and grow closer as friends throughout this adventure.
One possible plot could be that Captain America is in a situation where he accidentally injures a fan during a chaotic battle. Maybe he's fighting a powerful enemy in a crowded area and his shield goes astray. He then feels extremely guilty and tries to make amends by using his resources to help the injured fan recover. He might also face public backlash for the incident which adds to his internal struggle.
In this fanfiction, he could also meet his past self. It would be an interesting encounter. They might have a conversation about his future experiences and how to better protect the world. And he may use his knowledge of the future to train his past self, making him an even better hero.
The Night King could be a great antagonist. His army of the dead and his own powerful magic would pose a huge threat to Captain America. Cap's used to fighting human foes, but the Night King is something entirely different.
One possible plot could be that they meet in an alternate universe where timelines have merged. Captain Carter and Captain America initially have a bit of a misunderstanding as they come from different versions of heroics. But then they realize they share the same values of justice and freedom. They team up to fight a common enemy that is threatening both their worlds, like a powerful time - traveling villain who wants to rewrite history to suit his evil plans.