I guess you've tried this method: Counting and rasterizing polygon overlaps in ArcGIS Desktop?

16,400 polygons isn't that many. However, one potential solution is to simply do a regular Spatial Join. In the ArcMap toolbox, > Analysis Tools -> Overlap -> Spatial Join.

Set both the target and join features to the same dataset and specify an output. Leave the rest of the settings.

After a few moments you should get back a shapefile that contains a "join count" column. Subtract 1 from this (as obviously each feature should intersect itself), and that should be the number of "overlaps "(actually intersects) for each polygon.

I just performed it on

I guess you've tried this method: Counting and rasterizing polygon overlaps in ArcGIS Desktop?

16,400 polygons isn't that many. However, one potential solution is to simply do a regular Spatial Join. In the ArcMap toolbox, > Analysis Tools -> Overlap -> Spatial Join.

Set both the target and join features to the same dataset and specify an output. Leave the rest of the settings.

After a few moments you should get back a shapefile that contains a "join count" column. Subtract 1 from this (as obviously each feature should intersect itself), and that should be the number of "overlaps "(actually intersects) for each polygon.

I just performed it on