One interesting crossover could be Stewie from Family Guy getting his hands on a Harry Potter wand and causing chaos at Hogwarts. He might use his advanced intellect to try and outwit the wizards and witches there.
In some fanfictions, there could be a plot where the dark magic in the Harry Potter universe intersects with the Addams family's natural inclination towards the macabre. Maybe a dark wizard tries to use the Addams family's home as a base for some evil plan. But the Addams family, with their own brand of strength and eccentricity, turn the tables on the wizard. This could lead to an alliance between the Addams family and the Hogwarts faculty to fight off the common threat.
Imagine Pugsley Addams getting a Hogwarts letter. He'd be so excited to learn magic, especially dark magic. He could get into trouble by trying to create his own spells inspired by the Addams family's unique interests. Meanwhile, the Addams family's butler, Lurch, could be a half - giant like Hagrid. He could interact with Hagrid and they could share stories about taking care of strange creatures.
One interesting crossover could be the Addams family's spooky mansion being a hidden location in the wizarding world. Maybe the ghosts in the Addams family mansion are actually the result of some botched wizarding spell long ago.
A more complex plot could be that the entire Family Guy cast gets transported to Hogwarts during a school year. Quagmire could be the new Defense Against the Dark Arts teacher, bringing his own unique brand of 'defense' which mostly involves flirting with the female students. Lois could get into trouble for trying to organize a Muggle - style PTA at Hogwarts, and Peter could end up on the Quidditch team as an accidental addition.
There could also be a scenario where Harry Potter has to face the Joker in a psychological battle. Since Harry has faced his own share of dark forces, the Joker's mind - games could be a new and different kind of challenge for him. Harry would have to use his courage and the skills he learned at Hogwarts to outwit the Joker.
One interesting crossover could be the use of magic in the Warframe universe. For example, a Harry Potter character might bring spells like 'Accio' to retrieve items in the middle of a Warframe mission. Or perhaps a Warframe with magical abilities inspired by Hogwarts magic.
One interesting crossover could be a Creepypasta character infiltrating Hogwarts. For example, Jeff the Killer could be lurking in the Forbidden Forest, adding a terrifying element to the otherwise magical place. It would be a really spooky scenario as students unknowingly get closer to this dangerous figure during their adventures in the forest.
One interesting crossover could be a scenario where Alucard uses his vampiric powers to assist Harry in a battle against Voldemort. Maybe Alucard's super strength and ability to transform could give Harry an edge in a difficult fight.
Well, a cool crossover might involve the Grimm from RWBY being affected by the magic in Harry Potter. Maybe the Death Eaters could team up with some of the more evil forces in RWBY. Also, the different houses in Hogwarts could be compared to the teams in RWBY. For instance, Gryffindor's courage could be related to Team RWBY's fearless nature.
A great crossover idea in the fanfiction could be a Quidditch match between Hogwarts and Alfea. The flying skills of the Winx fairies would add a new dimension to the game. And the strategic play of the Hogwarts students would also be interesting to see in combination. Also, the different brooms and flying devices could be compared and contrasted.