One idea could be that the characters from Persona 5 end up in the Harry Potter world. They could use their Personas to fight against the dark wizards. For example, Joker could use Arsene to take on Voldemort's Death Eaters.
Maybe the Hogwarts students discover the power of Personas. Harry, Ron, and Hermione could learn how to awaken their Personas and use them to solve mysteries within the castle, like finding out who is behind a series of strange disappearances in the Forbidden Forest.
Maybe the Velvet Room attendants from both games somehow get their worlds mixed up. Igor from Persona 5 and Margaret from Persona 4 have to work together to set things right. This leads to the characters from both games interacting. The Phantom Thieves might learn some new combat techniques from the Investigation Team and vice versa. They could then use these new skills to face a common threat that emerges from the merging of their two realities.
Some Harry Potter persona fanfiction stories play with the idea of the Death Eaters having different personas. Maybe Bellatrix is not as completely evil as she seems, and there is a reason for her loyalty to Voldemort that is more complex. Or Lucius Malfoy having a change of heart and trying to redeem himself through helping the good side. There are also fanfictions that explore the personas of the minor characters, like Neville Longbottom becoming a powerful and respected wizard much earlier in his life.
Well, perhaps the story could start with a strange distortion in the Metaverse that links the two universes. Some of the characters from Persona 4 start having dreams about the events in Persona 5's Tokyo, and vice versa. This leads to a meeting between the two groups. They then discover that an ancient evil, long forgotten in both their histories, is trying to use the connection between the two worlds to gain enough power to rule over everything. The characters would have to learn about each other's powers and personalities quickly in order to stand a chance against this new foe.
Perhaps the fanfiction focuses on the cultural clash between the two groups. The Persona 4 characters are from a small town, while the Persona 5 crew is from the big city. Their different ways of handling things and their unique Personas could lead to some interesting interactions. For example, Yu and Joker might have different leadership styles that they have to reconcile in order to succeed against the shadows.
A great plot could be that a new threat emerges that has the power to erase the memories of people in both Persona 4 and Persona 5's worlds. The characters from both games must work together to find the source of this threat. The Phantom Thieves could use their infiltration skills, while the Investigation Team could use their detective - like skills to gather clues. As they progress, they discover that the root of the problem lies in an ancient evil that was once sealed away but has now been awakened due to some modern - day events.
Well, perhaps the Omnitrix gets mixed up with the magic in Hogwarts. It starts malfunctioning and instead of the usual alien forms, it gives Harry forms of ancient wizards. He has to figure out how to control these new forms while also dealing with the mystery of why the Omnitrix is acting this way. And he might learn new spells and magic from these wizard forms.
One idea could be that Palpatine somehow discovers the wizarding world of Harry Potter. Maybe he sees it as a new realm to conquer. He could try to manipulate the Ministry of Magic using his Sith mind - tricks, and Harry Potter would have to figure out who this strange new threat is and stop him. It would be a clash of two very different kinds of magic.
Maybe in the 'Harry Potter in Undertale fanfiction', Harry discovers that Voldemort has also found his way into the Undertale world and is trying to gain power there. Harry has to learn the rules of this new world quickly. He befriends Sans and Papyrus. Sans, with his knowledge of the resets in Undertale, helps Harry understand how to manipulate time in a way that could give him an edge against Voldemort. Papyrus, on the other hand, is enthusiastic about Harry's magic and they train together to fight off Voldemort's minions in the Undertale world.
Another plot could be that Voldemort discovers Powergirl's existence and sees her as a threat. He tries to manipulate the wizarding world against her. But Harry and his friends believe in her and together they work to expose Voldemort's lies and also learn from Powergirl about different ways of fighting evil. Powergirl could introduce new concepts of justice and heroism to the wizarding world.
One possible plot is that Harry, as a blacksmith, is sought after by all the magical communities. He could create a new kind of portkey that is not only more stable but also has the ability to transport large groups of people at once. His blacksmithing skills could also be used to create a device that can detect dark magic from a distance. This would make him a valuable asset in the wizarding world. He could also hold blacksmithing workshops at Hogwarts, teaching the younger students the art of creating magical items, which would be a great way to pass on his skills and knowledge.