The interaction between phonons and localized plasmons in coupled nanoparticles can be exploited both for modulating the scattered electromagnetic field and the understanding of the mechanical vibrations at nanoscale. In this paper, we demonstrate by numerical analysis an enhanced optomechanical interaction in a film-coupled gold dimer nanoparticles mediated by surface acoustic waves. Two gold nanoridges are placed atop a multilayer structure consisting of a thin dielectric spacer covering a gold film layer on a silicon dioxide substrate. Numerical simulations of the optical properties reveal the existence of three surface localized plasmons in the infrared range with enhanced scattering and narrower linewidths than with a single nanoridge. The physical origin of such modes as well as their tunability as function of key geometrical parameters are successfully captured with a simple model based on effective Metal-Insulator-Metal (MIM)-like plasmonic cavity. We calculate the optomechanic coupling rates between the GHz localized mechanical modes and plasmonic modes of the dimer, finding that the strongest coupling is observed for the in-phase compressional mode followed by the out-of-phase flexural mode. Both such modes can be excited by launching a surface acoustic wave (Sezawa wave) at the inlet in front of the dimer structure. It is also found that the flexural mode which is inactive optomechanically in case of a monomer becomes active due to dimer coupling, with a significant phonon-plasmon coupling rate. The findings in this work may facilitate design of new optomechanical components monitored with fast coherent acoustics, leading to new generation of light acousto-optic modulators where strong optomechanical interactions are required.