Boo would probably interact with the baby monster in a very gentle and affectionate way. She might hug it a lot and try to communicate with it using her own unique baby language. Since she's a child herself, she would likely see the baby monster as a new playmate and would share her toys with it.
Maybe in the fanfiction, Sulley discovers that Randall has a hidden side. Randall might be secretly trying to protect the monsters from a new threat in the human world that no one else is aware of. Sulley initially doubts Randall but as he sees the evidence, he decides to help Randall. They then team up and use their different skills - Sulley's big and strong nature and Randall's sneaky and intelligent ways - to overcome the threat and in the process, their relationship changes for the better.
It's also because their personalities are so different yet complementary. Sulley is big and strong while Mike is small and smart. Fanfiction writers can play with these characteristics in various ways. For example, they can create stories where Mike's ideas and Sulley's ability to execute them lead to amazing results. This contrast makes for interesting and engaging stories.
One good example could be fanfictions that focus on their adventures outside of work. For instance, a story where they go on a trip to a new, uncharted part of the monster world. Another might be ones that explore their friendship during their childhoods, like how they first met at monster school.
It could be about Boo using her experiences in the monster world to make a difference in the human world. Maybe she becomes an advocate for better understanding between humans and monsters.
A possible plot could be that there's a baby monster that is scared of everything in Monsters Inc. Boo, who has experienced the monster world, takes it upon herself to show the baby that there's nothing to be afraid of. She introduces the baby to all the friendly monsters she knows. Sulley and Mike are a bit skeptical at first but soon see how Boo's kindness is helping the baby grow braver. As time goes on, the baby becomes more confident and starts to explore the world on its own with Boo by its side as a guide.
In a different take, Sulley and Randall could be partners in a secret experiment within Monsters Inc. They might be working on a new way to collect energy from kids without scaring them. As they work closely together, they discover that they have a lot in common when it comes to their love for the monster world and their hopes for its future. This shared passion could lead to a deeper bond between them, different from the adversarial relationship in the movie.
By showing how her time in the monster world influenced her values. For example, if she learned about kindness from Sully, as an adult she could be extra empathetic.
Friendship is a very common theme. Since the OC is a new character, often the story focuses on how they become friends with Sulley. For example, they might help each other out in tricky situations at Monster Inc.