ArcGIS Spatial Join - "contains part of" match option

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I would like to performs a spatial join using a (non-existent) "contains part of" match option. i.e. I want the join to include any and all polygons that overlap. None of the match options available produces satisfactory results.

To clarify, using the ESRI graphics ("Select polygon using polygon" examples at the bottom), I would like the join to apply to examples A, C, E, F, G, H, K and M ONLY.

The result I am interested in is the the join count per polygon

Any ideas for a work around or is there another tool that will do this?

Thanks



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