One idea could be exploring a different faction's perspective in more depth. For example, showing the daily life and hidden secrets of the Amity faction. Another could be creating a new character who has unique abilities and seeing how they fit into the Divergent Games world.
Maybe the factions from Divergent are incorporated into the districts of the Hunger Games. The Dauntless could be in a district known for their fighting skills and they might rebel against the Capitol's rules for the Games. The Erudite could try to use their knowledge to find a way to stop the Hunger Games altogether. And the main characters from both stories could team up to fight against the oppressive systems.
A cool fanfiction idea could be that the world of Divergent and the Hunger Games are actually two parts of a bigger experiment. The main characters from both universes start to discover this connection during a Hunger Games where some strange, Divergent - like abilities start to show up among the tributes, and they have to figure out what's really going on.
One popular idea is crossovers. For example, imagining characters from Hunger Games in the world of Divergent or vice versa. Another idea could be exploring different 'what if' scenarios. Like what if Katniss from Hunger Games was in a different faction in the Divergent world. Also, fanfics often focus on the backstories of minor characters from both series.
One interesting plot idea is the crossover of the unique skills from both worlds. For example, in some fanfictions, the Dauntless' fearless fighting skills are combined with the survival skills of the Hunger Games tributes. It creates really intense and exciting battle scenes.
There might be a fanfiction where two characters from Divergent Games who were once enemies end up having to team up. Maybe a Dauntless and an Erudite. They start to understand each other's worlds and in the process, fall in love. This creates a whole new dynamic in the Divergent Games universe.
One idea could be exploring what would happen if Tris survived the final battle and had to rebuild the society in a completely different way. Another could be a story from Four's perspective during his early days in Dauntless before Tris arrived.
One interesting crossover could be characters from Divergent being thrown into The Hunger Games arena. For example, Tris could use her Dauntless skills to survive in the Games. Maybe she'd form an alliance with Katniss, and together they'd come up with new strategies that combine their different worlds' fighting and survival techniques.
Some cool concepts in Hunger Games fanfiction involve changing the rules of the games. What if there were no mentors? How would the tributes fare? In Divergent fanfiction, there's often a focus on characters who are Divergent in different ways than Tris. It could be someone who has a more extreme form of being Divergent and how they navigate the society. Another aspect in Hunger Games fanfic is the exploration of the Capitol's inner workings from a different perspective, not just the rebels' view. And in Divergent fanfic, imagining new initiation processes for the factions that test different qualities can be really engaging.
One idea could be a fanfic about a magical foot race where the participants have special powers related to their feet. Another could be a story set in a world where foot games are used to solve disputes among different tribes. Maybe a fanfic about a young athlete who discovers a new foot game that changes his life.
One interesting 'divergent fanfic' could be one that explores an alternate ending where Tris and Four end up leading different factions together instead of just Dauntless. It gives a whole new perspective on the faction system and their relationship.