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.
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.
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.
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.
One idea could be the characters from Persona 4 and Persona 5 swapping their worlds. So the Phantom Thieves end up in Inaba and have to deal with the Midnight Channel mystery. And the Investigation Team finds themselves in Tokyo and gets involved in the Metaverse. It would be really cool to see how they interact with the different environments and characters.
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.
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 really interesting plot could involve a new threat that emerges and can only be defeated by combining the powers and skills of the Persona 3 and 5 characters. For example, the combat styles of the two groups are different. The SEES members are more used to fighting in the Dark Hour, while the Phantom Thieves operate in the cognitive world. They would need to learn from each other's strategies. And on a character level, the more serious and reserved characters from Persona 3 could interact with the more flamboyant and confident characters from Persona 5, leading to some really interesting dialogue and relationship building.
Maybe there's a situation where the Velvet Room attendants from Persona 3, 4, and 5 realize that there's a threat to the collective unconscious that only the combined efforts of the three protagonists can stop. So, they somehow manage to bring the characters together. The characters then start to learn from each other's combat styles and ways of forming bonds with their friends, which helps them in their fight. For example, the protagonist of Persona 3 could teach the others about his experiences with death and how to face it head - on in battle, while the Persona 4 protagonist could share his knowledge of reading people and finding the truth behind the mysteries. The Persona 5 protagonist could contribute with his skills in stealth and infiltration.
A great plot for Persona 4 crossover fanfiction could be a crossover with the 'Sword Art Online' universe. The Persona 4 gang could be trapped in the virtual world of SAO and have to use their Personas to defeat the bosses and escape. Or, they could cross over with the 'My Hero Academia' world. Here, they could attend the hero school and learn new ways to use their powers, while also sharing their Persona knowledge with the MHA characters. Also, a crossover with 'Harry Potter' would be interesting. They could attend Hogwarts and discover that their Personas have unique interactions with magic.
A crossover with a post - apocalyptic world setting. The Persona 3 characters find themselves in a world destroyed by some great cataclysm. They have to use their Personas not only to fight the Shadows that lurk in this new world but also to survive against other desperate survivors and new, mutated threats. They might also have to find a way to restore the world using their Persona powers.