We present a compact and multi-resonant aperture system supporting large local electromagnetic fields, which is highly advantageous for applications demanding high signal-to-noise ratio. The system is composed of subwavelength H-shaped apertures with extended arms fabricated through thin metal films on a free-standing dielectric membranes. Through finite-difference time-domain calculations, we numerically investigate the multi-resonant spectral nature of the compact system in detail, which is associated with the individual optical response of the constituting aperture elements. In order to realize the aperture systems working in the spectral region of interest, we introduce a fine-tuning mechanism of the optical responses through geometrical device parameters. Furthermore, we present a circuit analog of the system demonstrating the impedance characteristics of the plasmonic modes supported by the aperture arrays. The highly accessible large electromagnetic fields extending over a large volume improve the sensitivity of the nanostructured platform to the surface conditions by enhancing the overlap between biomolecules in the vicinity and the local optical fields. We also experimentally demonstrate this highly advantageous field generation capability through large absorption signal enhancements in the surface enhanced infrared absorption spectroscopy of protein bilayers.