arcgis desktop - Splitting all polygon features in a shapefile into smaller equal width polygons

I have a shapefile of thousands of polygon features, that i would like to break up into smaller pieces (i.e. break a square into 8 equal pieces). I have read all over these boards for the right solution and haven't found one yet unfortunately. I've tried parcel editor but that only allows you to manually edit one feature at a time, and I've tried fishnet but that doesn't run through each individual feature it just processes across the entire extent of the shapefile. I have the full license for ArcGIS so all options are game. Ultimately I would like to be able to split this initial shapefile of features into a specified amount of equal width slots that each would be their own feature in the resulting shapefile.

Any thoughts?