This Letter discusses nonresonant modes excited on holey metasurfaces and their influence on the properties of spoof plasmonic states supported by the metasurface when a second surface is placed in its proximity. We consider here a metallic surface with periodic holes drilled in it. The field excited on each hole is projected onto a set of nonresonant modes in order to discuss their relative relevance. While previous simpler models assumed only the presence of the fundamental mode, we show that the simultaneous presence of several modes occurs when the surface is placed next to a metallic plate. Therefore, higher-order modes are responsible for the peculiar physical properties of wave propagation of spoof plasmons between two surfaces, which can lead to new gradient-index flat lenses for transceivers for space communications.