Multisite child theme header and footer consitency

For a mult-isite installation using sub-directory sites set up to maintain the same design as the parent site using separate child themes. How do you maintain control over a headers and footers of the all the separate child themes in one place because each child theme has separate functionality for each sub site. One analogy is that you have a “Male Parent" theme that you don’t want to alter because the developer releases updates and any changes you make will get over written. So Now I am seeing a need for a “Female Parent” theme that maintains multi site constant settings allowing site wide theme changes spawning the updates to the “Child themes” Is there is a simple solution to this issue as currently if I change the header color in one site I have to go through the other 10 and update each child theme manually…… Appreciate any help