Hi Chad,
It should be as easy as installing multiple child themes and activating each different one on each site individually.
There’s no naming rules, the top of your style.css just needs to reference the parent theme like this:
/*
Theme Name: GeneratePress Child
Theme URI: http://generatepress.com
Description: Default GeneratePress child theme
Author: Thomas Usborne
Author URI: http://edge22.com
Template: generatepress
Version: 0.1
*/
The only thing above that’s crucial is: Template: generatepress