I am working on a character that has fins for ears, and have set the fin membranes geometry to a vertex group, then added a Solidify modifier to the mesh to only affect the membranes vertex group.
The membranes now have thickness, but the modifier has caused rest of the mesh to zero thickness faces z-fighting all over the non-membrane geometry
You can see the effect this causes in this image (the ear fin is a separate mesh from the rest of the head).
Adding a value of 0.001 to the Factor field helps a little with the z-fighting, there are still issues where the geometry is shrinkwrapped to the head, as Z-fighting still occurs there, regardless of whether the Shrinkwrap modifier is before or after the Solidify one, and the Data Transfer modifier to blend the fins mesh with the head doesn’t overwrite the z-fighting.
I’ve tried using a Decimate modifier after the Solidify modifier to try to collapse the zero thickness geometry, but no settings I tried there helped any. Looking for any other ways to manage eliminate this problem geometry, or at least mitigate the z-fighting issue.

