Friends To All Children: The monsters can often be found playing with human kids and offering them fun experiences due to their great sizes.
From Bad to Worse: Inverted with One's reasons to tell on her sibling during the campout in the episode I'm Telling! At first, One has good reasons to tell on them, like Four planning to have Seven climb up an incredibly unstable stack of books to reach an ENORMOUS suitcase for Six to pack a bunch of clothes that she does not need at all for one night in the backyard and use Five as a safety landing, and then Four planning to pack everything in the fridge to take to eat on the campout. But then she starts telling on them for smaller and smaller things like Four not sharing the snacks, Seven yelling at her when she tries to help, and Six sticking her tongue out at her. Mom even lampshades this:
Mom: (sighs) One..maybe these things are not all that serious being.
Furry Female Mane: Both One and Six have human-like hair despite being furry (although Six's face isn't). Three also has a mop of human-like hair, however, as do Two and Seven (though they don't look furry).
In Name Only: The monsters share the same names and basic designs from the original picture book by Maurice Sendak, but the series is otherwise unrelated to it.
It's a Wonderful Plot: Inverted in "It's A Wonder-Four Life". Four wishes he didn't have siblings, and is shown a world where he is an only child and everything is about him. After what should have been a perfect day for him, he winds up feeling lonely, which makes him appreciate his siblings more.