edit the models themselves?
a part
use one base body for every character and simply replace the head?
a part
Is it possible that they are using common MMD models but making them look different through shaders, materials, or other modifications?
yes
You gotta add mmd support onto said model, use blender and do the mmd blenshape, there should be a tutorial somewhere, i could try to help but i don't have time lately, sorry!
