Batch matching background tone and color for headshots?

We create yearbook photos and images always have variation in tone and color in the background.  The background masking works wonders now on an individual image but is there a way to batch balance the background on multiple images so they are near the same tone and color?  I'm attaching a contact sheet with 4 images before and after. This is what I'm doing manually and while not perfect, obviously much closer.  Is there anyway to batch automate this process or get it somewhat close?  I would gladly by a coffee for anyone that can help find a solution for this, if there is 🙂