I heard that Randall has a nephew named "Rex" from the Monsters Inc. Storybook Collection, one of the monster toddlers staying in the company's daycare program. So I have created the idea for Monsters Inc AU:
Rex Boggs is a a Lamian-Reptilian monster toddler who is a best friend of Boo/Mary Gibbs. Turns out, he is also Randall's nephew. Because his parents are working outside Monstropolis, Randall practically raised him as his own. Rex's relationship with his uncle is quite positive as he was pampered with baked goods his uncle would make for him. The little Lamian-Reptilian toddler looks up to his uncle and views him as his "#1 Scarer".
At one point, by the time Boo got acquainted with the Monster Inc since her sudden appearance in Monstropolis, she met Rex who was curious of human toddler. In fact, the two developed close friendship. Randall was frustrated of inability to separate the human child from his nephew, knowing fully well that would highly upset Rex if he did. Rex is often seen teething on empty canisters, Monster inc helmets, etc.
Michelle Wazowski & James Sullivan: When the duo took the assignment to be the caretakers of monster toddlers, they met Rex who used his invisibility and camouflage to surprise them. After encountering Boo, the two realized if they let Boo stay with him, Randall won't hurt the kid and allowed the two toddlers to bond.
Boo/Mary Gibbs: Initially confused of one another, the two curiously approached each other. Boo refers him as "Rexy", a friendly nickname she came up for him. When they had to say goodbye, Rex cried all day and night as Randall struggled to calm his nephew, panicking when Rex threw a fit saying he might die if he "cannot see Boo forever". Begrudgingly, pushing his pride aside, Randall backed off whenever Rex and Boo meet and play together.
Randall Boggs: Rex is very attached to his uncle ever since he was born, forming a father-son bonding. Every time Randall was yelling or reprimanding Fungus, stressing over being the 2nd place at Scare Rank, his sour expression changes when Rex happily waddle/slither fast to him. Spoiling him, Randall bakes/cooks whatever his nephew wants. One occasion Randall's score skyrocketed was when Sid Philips (one of the kids Randall scares) spotted Rex and roughly handled him causing Randall to snap and traumatized the personality-questionable human kid to the point of putting Sid's head in his mouth until he was stopped by the other scarers, as Randall would DEVOUR anything that is a threat to Rex.
Jeff Fungus: As Fungus was Randall's assistant, he is acquainted to Rex. While Fungus was incompetent as scare assistant, he knows how to make Randall's nephew laugh. During the "take the kids to work" day, he was seen carrying Rex while Randall would continue his duty. Fond of the toddlers in nature, Jeff Fungus happily took the job as Monster Inc daycare program's teacher, finding Rex and Boo's friendship wholesome and adorable.
In Disney/Pixar/Don Bluth/Dreamworks Studio AU: Alongside Boo/Mary, he was a toddler starring in the Monsters franchise series and was typically seen running around the studio with Boo, only to nap later with her as Sulley and Randall would take a lot of pictures of them. Currently, as pre-teen/teenager, he remains as close friend with Boo, sharing same hobbies. According to Maxine Goof and others, Rex was often bullied for hanging out with a girl but Boo would retaliate in his defense.