One possible plot could be that Wolverine somehow gets transported to the wizarding world. He could be mistaken for a dark creature at first because of his claws and rough appearance. But then he teams up with Harry Potter to fight against a new dark wizard who has the power to control metal, which poses a great threat to both the Muggle and wizarding worlds. Wolverine's healing factor and combat skills, combined with Harry's magic, would make for an exciting adventure.
One possible plot could be that Wolverine somehow ends up in the Twilight universe. Maybe he's on a mission that goes wrong and he gets transported there. He then meets the vampires and werewolves in Twilight. The vampires might be intrigued by his healing factor and his adamantium claws. And the werewolves could see him as either a threat or an ally. He could get caught in the middle of the conflict between the Cullens and the Volturi, using his combat skills to tip the balance.
Well, perhaps the magical creatures from the Harry Potter universe end up in the '300' setting. Dragons could be used by the Spartans to fight their enemies. The centaurs could also join the battle, lending their archery skills. And Harry could learn some combat skills from the Spartans, which he could then use back in the wizarding world to fight Voldemort's Death Eaters.
In this fanfiction, perhaps Harry Potter's grandson inherits Wolverine's adamantium claws through some sort of magical - mutant genetic quirk. He has to keep this a secret from the wizarding world at first, but as he grows older, he realizes that he can use these claws and his wizarding skills together to fight dark wizards and mutant villains alike. He becomes a bridge between the two worlds, trying to create peace and understanding between mutants and wizards.
The Stargate could be a portal between different magical realms in the Harry Potter universe. For example, it could lead to a place where ancient and more powerful magic exists. Wizards from different schools around the world could team up with Stargate explorers to uncover the secrets of this new place. There might be a new threat emerging from this realm that requires both magic and Stargate technology to defeat. This would bring together characters like Harry Potter and Jack O'Neill to lead the charge against the common enemy.
Well, perhaps there's a rift in the multiverse that connects Central City to Hogwarts. The Flash, while chasing a villain, gets sucked into the wizarding world. Harry Potter and his friends initially suspect him as a threat but then realize his good intentions. They then combine their powers - the Flash's speed and the magic of the wizards - to fight a common enemy. For example, the Flash could use his speed to distribute protective spells all over Hogwarts really quickly, while Harry and his friends focus on the offensive magic against the bad guys.
One idea could be that Carly and her friends discover a magical portal in their apartment that leads to Hogwarts. They then have to navigate the wizarding world, with Carly being fascinated by all the magic. Meanwhile, Harry Potter and his friends are intrigued by the strange Muggle - like devices the iCarly gang has. They end up teaming up to solve a mystery that involves both the wizarding and Muggle worlds.
Well, perhaps the Death Note from the Bleach universe gets mixed up with the magic in Harry Potter's world. A powerful wizard could get hold of it and start using it in ways that disrupt the balance of life and death in both worlds. Harry and his friends would have to figure out how to stop this misuse, with the help of some Bleach characters who understand the true nature of the Death Note.
One idea could be that Eragon, while on one of his adventures in Alagaësia, accidentally creates a portal that leads him to Hogwarts. There, he meets Harry Potter and they quickly realize they have a lot in common. They could team up to fight against a dark force that somehow threatens both their worlds, like a new type of dark magic that combines the magic of Alagaësia and the dark arts from the wizarding world.
In a more comical plot, Hagrid could accidentally stumble upon a small Transformer while in the Forbidden Forest. Thinking it's a strange magical creature, he brings it back to Hogwarts. The Transformer, being a bit lost in this new magical world, causes all sorts of chaos in the castle. Harry and his friends have to figure out how to get the Transformer back to where it belongs while also dealing with the daily challenges at Hogwarts.
One possible plot could be that the Duel Monsters from Yu - Gi - Oh! are introduced to the wizarding world of Harry Potter. Wizards start using them in duels instead of their traditional spells. Harry and his friends have to learn the new rules of these duels and face off against a dark wizard who has mastered the most powerful Duel Monsters.