We present a detailed structural and surface-enhanced Raman scattering (SERS) study of poly(allylamine) modified with Os(byp)2ClPyCHO (PAH-Os) and gold nanoparticles self-assembled multilayers [PAH-Os+(Au-nanoparticlesPAH-Os)n, n=1 and 5]. Atomic force microscopy and variable-angle spectroscopic ellipsometry measurements indicate that the first nanoparticle layer grows homogenously by partially covering the substrate without clustering. Analyzing the sample thickness and roughness we infer that the growth process advances thereafter by filling with nanoparticles the interstitial spaces between the previously adsorbed nanoparticles. After five immersion steps the multilayers reach a more compact structure. The interaction between plasmons of near-gold nanoparticles provides a new optical absorption around 650 nm which, in addition, allows a more effective SERS process in that spectral region than at the single-plasmon resonance (approximately 530 nm). We compare the electronic resonance Raman and SERS amplification mechanisms in these self-assembled multilayers analyzing Raman resonance scans and Raman intensity micromaps. As a function of nanoparticle coverage we observe large changes in the Raman intensity scans, with maxima that shift from the electronic transitions, to the plasmon resonance, and finally to the coupled-plasmon absorption. The Raman micromaps, on the other hand, evidence huge intensity inhomogeneities which we relate to "hot spots." Numerical discrete dipole approximation calculations including the interaction between gold nanoparticles are presented, providing a qualitative model for the coupled-plasmon absorption and redshifted Raman hot spots in these samples.