Saber from Fate/Stay Night would be an obvious choice. Since she is also related to the Arthurian legend, there could be a lot of interesting interactions between them. They could compare their experiences as king, or even fight side by side against a common enemy.
One common theme is the clash of cultures. For example, when Arthur crosses over into a modern or alien world, his medieval values and the new - found values of the other world collide. Another theme is the test of leadership. No matter where he is, Arthur is often put in situations that test his leadership skills.
One idea could be an Arthur crossover with the world of Alice in Wonderland. Arthur could find himself in Wonderland, meeting the strange characters and getting into all sorts of wacky adventures. Another could be a crossover with a superhero universe, where Arthur gains superpowers and has to save his world from a new threat. A third idea might be an Arthur crossover with a historical setting, like the Middle Ages, where he has to adapt to the different time period and its challenges.
The theme of redemption also pops up. If Arthur is placed in a darker or more morally ambiguous world, his quest for justice and honor can be seen as a form of redemption for the new world he's in, or it can be a test of his own values as he faces new challenges.
To start an Arthur crossover fanfiction, you need to do research on both Arthur's world and the world you want to cross it with. If it's a crossover with a sci - fi world, learn about the common tropes in sci - fi. Then, think about how Arthur's personality will be affected by this new world. Will he be scared? Curious? After that, come up with a conflict. Maybe in the crossover world, there's a tyrant and Arthur has to help the resistance. Start writing the story with a strong hook to draw readers in.
In such a crossover, perhaps Harry Potter could use his magic in Camelot. He might help King Arthur fight against dark magic threats that Camelot faces, like Morgana's sorcery. His spells could be a new weapon in Arthur's arsenal.
You can start by looking on popular fanfiction websites like Archive of Our Own (AO3). Just search for 'Arthur Morgan crossover' in the search bar, and it'll show you a bunch of relevant stories. Check the ratings and reviews to see which ones are highly recommended.
There's also 'Arthur and the Star Wars Galaxy'. This one is a wild ride where Arthur Pendragon somehow ends up in the Star Wars universe. He teams up with Jedi and Sith, and his code of chivalry creates some unique interactions within the Force - using world.
One idea could be that Arthur crosses over into a world where the Invisibles are facing a new and powerful enemy. He uses his human creativity and skills to help them find a solution. For example, he might introduce new technologies or ways of thinking that the Invisibles haven't considered before.
One great 'King Arthur Crossover Fanfiction' is 'King Arthur in the Modern World'. It's really interesting as it shows how Arthur and his knights adapt to modern life, with Arthur working in an office and still trying to uphold his chivalric values. Another one is 'King Arthur Meets Merlin in a Different Realm' which plays with the idea of alternate universes and their relationship in a new setting.