We propose and show multispectral optical enhanced transmission in the visible and near-infrared region in a continuous metal film coated with a two-dimensional (2D) hexagonal non-close-packed plasmonic array. The plasmonic array consists of metal/dielectric multilayer core-shell nanoparticles. The excitation of near-field plasmon resonance coupling between adjacent core-shell nanoparticles, plasmon resonance coupling between adjacent metal layers in the nanoparticle, and surface plasmon (SP) waves on the metal film are mainly responsible for the multispectral optical enhanced transmission behavior. The multispectral optical enhanced transmission response could be highly modified in the wavelength range, transparent bandwidth and transmission intensity by varying the geometry parameters including the gap distance between adjacent plasmonic nanoparticles, the size of metal core and the thickness of dielectric layer between the metal layers. In addition, the number of optical enhanced transmission bands increases with the number of metal layers in the plasmonic nanoparticle. The proposed structure shows many merits such as the deep sub-wavelength size, multispectral optical enhanced transmission bands as well as fully retained electric and mechanical properties of the natural metal. These merits may provide promising applications for highly integrated optoelectronic devices including plasmonic filters, nanoscale multiplexers, and nonlinear optics.