qgis - Create new polygon layer based on areas of varying numbers of stacked polygons

I have several species range maps (as polygons) that overlap/stack. From this, I am trying to identify areas of highest biodiversity. Ideally, I'd like to create a new polygon layer, where 1 part is the area where 20 ranges overlap, part 2 is the area where 19 ranges overlap, etc.

I am using QGIS and Spatialite as my primary tools.

Thanks for any help that might be offered.