Clipping with multiple overlapping polygons while maintaining unique IDs and overlap
I've got a series of square overlapping polygons. I want to clip a layer based on these polygons and maintain the unique ID and overlap of the polys. As it is now, if I do a clip using overlapping polygons, the clip will automatically merge all the unique polygons (see attached) by basically assuming the square polygons are one big mask. You can see that many of the square polygons overlap significantly and will have nearly identical clip results-which is exactly what I want. Aside from clipping one polygon at a time (there are 3,000+ of them), I cannot figure out a solution. There don't seem to be any options to tell ArcGIS to turn off the automatic merge.
Use Intersect and then Dissolve. See the result below of my use of these two tools. It duplicates the blue polygon for all overlapping square polygons and preserves the FIDs of both layers in new fields. A dissolve that includes both FID fields ends up with each original square's intersection with each blue polygon it touched. It works.