Same theme, different stylings

I'm probably misssing it or searching the wrong things, but I noticed after updating Atahualpa to the newest version, there is a theme images option and there is this text-

"For MULTI SITES, you should choose the 'wp-content' option and give each multisite a unique folder name like multi-01 and multi-02"

I understand by this that theme images such as backgrounds, headers, logos, favicons can be stored separately for each site using the theme in a multisite install. What I am unclear on is can I use a single version of Atahualpa across all of my sites but with different stylings? As it is right now, I have multiple copies of Atahualpa, one f reach site, that have been renamed and must be updated manually to have different stylings.