Since they are a part of the game you can plant from one group to the other relatively easily let's share some classmates (or other NPCs) we made and cool questions to ask about them during the setting creation part. Whatever worked great in your game or just cool ideas in general.
I had a character that I did not start out with a name but a vague description and the question: "What Nickname did you give her that stuck?" The followed up with questions about how well that Nickname was liked.
I put in an NPC whose dark secret was being a drug mule. But it could have been supernatural and got that character stuck at a murder scene without ever being able to tell anything about it without risking herself.
I will add a few more later once I talked with my players which they liked or more come to my mind by brainstorming.