I have looked throughout this site to find a method to calculate the overlap area of multiple polygons within a single shapefile but haven't found one that works for my case. I've tried the intersect tool but that doesn't seem to accomplish my task as it requires multiple input shapefiles.
Above I have included a image of my shapefile and the polygons. Each polygon represents an animal's territory and has several attributes assigned to it (age, sex, etc). In this example, there are some polygons (animal territories) that don't overlap and others that overlap multiple polygons. What I would like to do is to calculate the total overlap area (dark purple) within the shapefile. Eventually I would like to know the identities of all the animals that overlap each other. In the entire shapefile I have 300+ territories and multiple years of data so I need an approach that would be somewhat efficient.