The study of localized surface plasmons (LSPs) in nanoscale structures is an essential step towards identifying optimal plasmonic modes that can facilitate robust optomechanical coupling and deepen our understanding of light-matter interactions at the nanoscale. This paper investigates numerically, using the finite element method, LSPs modes in a design comprising two coupled nano-ridges deposited on a gold layer, with an interposing polymer spacer layer. Such a structure, usually referred to as particles-on-mirror, shows exquisite optical properties at the nanoscale. We first examine the LSPs modes of a single nano-ridge through the analysis of its scattering cross-section in the visible and infrared range. To enhance the plasmonic response, a thin polymer layer is placed at the middle of the ridge, which introduces additional LSPs modes confined within the former. Then, we extend the analysis to the dimer configuration, which exhibits more complex and enhanced plasmonic behavior compared to a single nano-ridge. In particular, the dimer configuration yields LSPs resonances with a quality factor enhancement of approximately threefold relative to single nano-ridge. Furthermore, the presence of the polymer layer within the ridges significantly improves plasmon field localization and quality factor. These findings underscore the potential of nano-ridge-based structures in advancing optomechanical coupling and plasmon-phonon interaction studies, offering valuable insights for the development of high-performance acousto-plasmonic devices. In particular, the proposed device could help significantly improve the design of nano-acousto-optic modulators operating in the visible or in the near infrared, that require enhanced light-photon coupling rate.