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.
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.
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.
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.
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.
One possible plot could be that the characters from RWBY end up in the Persona universe and have to learn how to use Personas to fight the Shadows. For example, Ruby could discover her Persona is related to her speed and scythe skills, and she uses it to quickly dispatch enemies. The team would also have to deal with the social aspects of the Persona world, like building relationships to strengthen their Personas.
The fanfiction could revolve around a new character who has the ability to traverse between the Splatoon and Persona 5 worlds. This character discovers a conspiracy that if not stopped, will merge the two worlds in a disastrous way. The character enlists the help of both the Inklings and the Phantom Thieves. They have to overcome their differences in fighting styles and cultures to save both their worlds. The inklings' turf war strategies could be adapted to the battles in the Metaverse, and the Phantom Thieves' stealth could be useful in the Splatoon world.
Maybe there's a strange distortion that merges parts of Inaba and Tokyo. The characters from both Persona 4 and Persona 5 find themselves in this strange new place. They start to notice that the Shadows in this merged world are more powerful and have new abilities. The Investigation Team and the Phantom Thieves must figure out how to adapt their Personas and strategies to fight these new threats while also dealing with the cultural differences between their two groups.
One idea could be that Mewtwo somehow gets transported to the Harry Potter universe. It could be mistaken for a very powerful magical creature. Harry and his friends could initially be wary of it, but then realize it has no intention of harm and they team up to fight against the dark forces in the wizarding world using Mewtwo's psychic powers.
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.