You can fit 3 12v batteries
I also do a lot of dry camping, and I have three kids who always have their laptops plugged into the inverter outlets. I installed a third 12v deep cycle battery in my motorhome last week. It was a tight fit, but it worked. I don't see how you could add a fourth battery. You mentioned that you are using 6v batteries. Perhaps if they are smaller than the 12v batteries you could fit four, but you would have to measure your batteries and the space to see if you could make them fit, especially since they have to be installed in pairs to get 12v.
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