How do I darken an area represented by overlapping shapes?

I have a bunch of objects that can overlap. These objects can be in front or behind (z-wise) other objects in the scene. I'd like to darken all the COLLECTIVE pixels behind a selection of these objects, without having them darken each other. I cannot have the shaded area be its own layer, unfortunately, as the shading can exist between objects in the main layer. Please see the photo below for a very simplified example.

Is this possible? How do I achieve this?