Fixing Bright Areas in Overlapping Meshes

Hi everyone, I'm very new to Unity and have looked on Google and here for an answer to my problem. I have a series of slightly overlapping meshes that make up a larger model. The areas of overlap in the model are much brighter in the render. See this example:

I am chopping the mesh into several parts because I need each part to have a texture that is 4096x906 is size.

Is there anyway to fix this in Unity? Any other suggestions are appreciated.

Thanks!