Two-dimensional multi-element phase gratings can be engineered to show an even symmetry along one direction while an odd symmetry along the other direction in terms of offset refractive indices in each unit cell. The interplay of such even and odd symmetries has been explored to tailor diffraction columns and rows on demand by making offset refractive indices to satisfy specific requirements and hence attain different types of destructive interference. The resultant tailoring effects include the directional column elimination, the grouped column elimination, and the directional column selection as well as the natural row absence, the grouped row elimination, and the central row selection.