Well, think about a scenario where the Philosopher's Stone gets stolen and taken to Asgard. Harry, Ron, and Hermione follow it there. Thor, initially suspicious of these strange wizards, eventually realizes they are on the same side. Together, they embark on a quest to retrieve the Stone, with Thor providing his brute strength and the Hogwarts gang using their wits and magic along the way.
One interesting crossover could be Darkseid's quest for the Deathly Hallows. Imagine him believing that these powerful magical artifacts could enhance his already great power. He might send his minions to Hogwarts to search for them, leading to a battle between the students and Darkseid's forces.
A possible crossover might involve Aragorn being magically transported to Hogwarts. He could be a bit bewildered at first by all the magic around him, but then he starts to adapt. He might end up training the students in physical combat skills, which are lacking in the wizarding world. Meanwhile, Harry Potter could be fascinated by Aragorn's tales of his adventures in Middle - earth and might even try to incorporate some of Aragorn's courage and honor into his own life.
Well, in some fanfiction, we might see Anna and Kristoff visiting Hogwarts. They could be amazed by the moving staircases and magical creatures. In reverse, Harry, Ron and Hermione could end up in Arendelle. Hermione might be intrigued by the way Elsa controls her ice powers and try to find a scientific or magical explanation for it. Also, the Dementors from Harry Potter could be compared to the dark forces in Frozen 2, like the mist that Elsa has to face.
One interesting crossover could be the use of magic in the Avengers world. For example, Hermione could use her knowledge of spells to help the Avengers solve a problem that technology couldn't. Maybe she could use a spell to break through an impenetrable force field created by an enemy. Another aspect could be the Avengers characters learning magic. Tony Stark might be fascinated by the concept of magic and try to incorporate it into his technology. Or Thor could share his knowledge of Asgardian magic with the Hogwarts students.
One interesting crossover could be a scenario where Hermione uses her magic to help Elsa control her powers better. Maybe she creates a spell that can soothe Elsa when she's about to lose control.
In some fanfiction, Maleficent might team up with a dark wizard from the Harry Potter universe. They could combine their powers to try and take over both the wizarding world and the fairy - tale land where Maleficent comes from. This would create a complex power struggle with the heroes having to find new ways to combat them.
One interesting crossover could be the characters from Harry Potter visiting Narnia. For example, Harry, Ron, and Hermione might find themselves in Narnia through some magical accident. They could then interact with the talking animals and magical beings there, like how they interact with the magical creatures in their own wizarding world. Maybe they would help the Narnians in a battle, using their unique Hogwarts - taught magic.
One interesting crossover could be the use of spells. For example, a Charmed one might learn a spell from the Harry Potter world like the Patronus charm. It could be used in a new and different way in the Charmed universe, perhaps to fight a new type of demon that is vulnerable to positive magic like a Patronus.
One interesting crossover could be Superman visiting Hogwarts. He might be amazed by the magic there. Maybe he tries to learn some spells, but his superpowers interfere. For example, when he tries to use a levitation charm, his super strength makes the object fly out of control.
One interesting crossover could be a scenario where Harry Potter and his friends encounter Janemba's chaotic powers in the wizarding world. Maybe Janemba's otherworldly abilities disrupt the magic there, and Harry has to use his knowledge of both magic and the strange new power he's facing to set things right. For example, he might combine spells with his natural courage to combat Janemba's minions.