A thin-film of dielectric on a reflecting surface constituting a multilayer substrate modulates light intensity due to the interference effect. A nanostructure consisting of randomly oriented silver particles of different shapes, sizes, and interparticle spacings supports multiple plasmon resonances and is observed to have a broad extinction spectrum that spans the entire visible region. Combining the two systems by fabricating the nanostructure on the thin-dielectric film of the multilayer substrate yields a new composite structure which is observed to modulate both the extinction spectrum and the SERS EF (surface enhanced Raman scattering enhancement factor) of the nanostructure as the thickness of the thin-film dielectric is varied. The frequency and intensity of the visible extinction spectrum vary dramatically with the dielectric thickness and in the intermediate thickness range the spectrum has no visible band. The SERS EF determined for the composite structure as a function of the thin-film dielectric thickness varies by several orders of magnitude. Strong correlation between the magnitude of the SERS EF and the extinction intensity is observed over the entire dielectric thickness range indicating that the extinction spectrum corresponds to the excitation of the plasmon resonances of the nanostructure. A significant finding which has potential applications is that the composite structure has synergic effect to boost SERS EF of the nanostructure by an order of magnitude or more compared to the same nanostructure on an unlayered substrate.