Photonic nanostructures with resonant modes that can generate large electric field (EF) enhancements are applied to enhance light-matter interactions in nanoscale, bringing about great advances in both fundamental and applied science. However, a small hot spot (i.e., the regions with strong EF enhancements) and highly inhomogeneous EF distribution of the resonant modes usually hinder the enhancements of light-matter interactions in a large spatial scale. Additionally, it is a severe challenge to simultaneously generate multiple resonant modes with strong EF enhancements in a broadband spectral range, which greatly limits the capacity of a photonic nanostructure in boosting optical responses including nonlinear conversion, photoluminescence, etc. In order to overcome these challenges, we presented an arrayed hyperbolic metamaterial (AHMM). This AHMM structure is applied to simultaneously enhance the three-photon and four-photon luminescence of upconversion nanoparticles. Excitingly, the enhancement of the three-photon process is 1 order of magnitude larger than previous records, and for the enhancing four-photon process, we achieve an enhancement of 3350 times, greatly beneficial for overcoming the crucial problem of low efficiency in near infrared light upconversion. Our results demonstrated a promising platform for realizing giant enhancements of light-matter interactions, holding potential in constructing various photonics applications such as the nonlinear light sources.