As stated in a few responses above, I managed to overcome this through resampling the raster to a finer resolution.
Ctrl-F > Resample > Choose the raster data from which values will be extracted per polygon > change the cell size to a much smaller number (1-5).
Then use the output from the Table of Contents in the Zonal Statistics function as before, and you should have many more of your values/unique identifiers.
Hi Anna,
You can do this with Zonal Statistics as Table. You just need to make a model that uses the Iterate Feature Selection iterator so that each of the overlapping polygons is passed into the zonal tool individually. You'll get an output table with 1 record for each polygon, then you run Merge to put the rows all back into one table. Then you join back to the polygons using the Zone Field you specified in Zonal Statistics as Table. Technically, you need two models. One that does the iterations on Zonal and collects all the values (the tables), and one that does Merge. You only want to execute Merge once, so this will be your main model, and the iterating model will be the sub-model. Please review the section called, "Advanced use of model iterators", within the help topic, Integrating a model within a model.
Best Regards,
Eric
There is a tool in this toolbox that separates the polygons into non overlapping groups, minimizing the number of iterations required (not brute force one at a time like that). Worth a try I think:
Introducing the Spatial Analyst Supplemental tools | ArcGIS Blog