A diffraction grating is a highly symmetric optical element with a physical structure that is invariant under translational spatial movements. The translational symmetry is reflected in the fields that are diffracted from the grating. Here, we introduce a plane-parallel mirror pair onto the grating, which translates the fields through double reflections, and we describe a method of exploiting the symmetry to enhance the spectral resolution of a diffraction grating beyond the limit that is set by the number of grooves. The mirror pair creates another virtual grating beside the original one, effectively doubling the number of grooves. Addition of more mirror pairs can further increase the effective number of grooves despite the increased complexity and difficulty of experimental implementation. We experimentally demonstrate the spectral linewidth reduction by a factor of four in a neon fluorescence spectrum. Even though the geometrical restriction on the mirror deployment limits our method to a certain range of the whole spectrum, as a practical application example, a bulky spectrometer that is nearly empty inside can be made compact without sacrificing the resolution.