In a Hufflepuff - Targaryen story, a Targaryen could be sorted into Hufflepuff. This would be an interesting contrast as Hufflepuffs are known for their loyalty and hard work, while Targaryens are often seen as more power - hungry. The Targaryen in Hufflepuff might have to learn to temper their desires for power and glory and instead focus on building strong, harmonious relationships within the house.
A fanfiction could also be centered around a magical artifact that links the two universes. Rhaegar and Harry Potter both get drawn to this artifact. They must work together to unlock its secrets. Rhaegar's knowledge of ancient magic and Harry's experience with the Dark Arts could complement each other in this quest, all while dealing with the political intrigue in both their worlds.
Perhaps in the fanfiction, Fem Harry Potter is a descendant of an ancient Targaryen who was sent to the world of Harry Potter for safety. When she returns to the world of Westeros, she meets Rhaegar. They could bond over their shared sense of duty. Rhaegar might be intrigued by her different kind of magic and her unique perspective on the world, and together they could work towards a more just Westeros.
One idea could be that Fluttershy somehow gets transported into the Harry Potter world. Maybe she arrives at Hogwarts as a new kind of magical creature that the students have never seen before. Her gentle nature might initially cause confusion among the more rowdy students, but she could gradually make friends with the likes of Luna Lovegood, who would be intrigued by her uniqueness.
Another concept could be that Harry Potter discovers he has a connection to Magneto's mutant powers. This might happen during a strange encounter with a dark magic object that unlocks a latent power within him. He then has to learn how to control these new abilities while also dealing with the threats in his own wizarding world, and he might seek out Magneto for guidance in a secret meeting across the boundaries of their two worlds.
One idea could be a crossover where Kakashi is summoned to the Harry Potter world by a dark magic spell gone wrong. He then uses his ninja skills and Sharingan to navigate the wizarding world, perhaps even teaching some Defense Against the Dark Arts classes with his unique combat knowledge.
Maybe in a fanfiction, Harry Potter and his friends accidentally stumble upon a hidden Cybertronian relic. This relic has some sort of power that attracts Megatron. Harry and his friends then have to defend the relic from Megatron while also trying to figure out what it does and how to use it to their advantage in the fight against Voldemort.
One idea could be a crossover where Harry Potter accidentally travels to the One Piece world and meets Whitebeard. He could learn about their different forms of magic and power, and together they face a new threat that combines the dark magic from his world and the powerful pirates in the One Piece world.
One idea could be a crossover where Harry Potter accidentally ends up in the world of Ranma 1/2. Maybe he's on a magical experiment gone wrong and lands in Nerima. He could use his magic to help Ranma deal with his curse, like creating a spell to keep him from changing into a girl when splashed with cold water.
Another concept could be a crossover where the magic in the Harry Potter universe has an unexpected effect on Android 18. For example, it could start to interact with her android systems in strange ways, giving her new powers or abilities that are a combination of magic and her android technology. This would lead to a whole new set of adventures as she tries to figure out what's happening to her.
One idea could be that Gandalf somehow gets transported to the Harry Potter universe. He could become a mentor to Harry, using his vast magical knowledge and wisdom from Middle - earth. Maybe he helps Harry understand some ancient magic that even Dumbledore wasn't fully aware of.