Best way to depict overlapping territories (polygons)

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I'm working on a set of maps that depict territories that overlap. The convention seems to be to use a solid fill on the lowest polygon in the stacking order and then apply a hatched fill to overlaps so that the underlying polygon is still visible. This approach works when you only have one overlap, but what about when you have three or more overlaps in different combinations? My initial reaction is to create a unique style for each scenario of three or more polygons. This approach generates more classes but reduces overlaps and clutter. Thoughts?

If anyone has any guidance or examples on how they approach this issue it would be greatly appreciated. Hopefully, my description makes sense. If it doesn't I can post a sample image and try again.

Cheers,
Erin


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