Here, it is demonstrated that similar chemical species within a multicomponent sample can be distinguished, down to the single-molecule level, by means of their surface-enhanced vibrational fingerprints. Surface-enhanced resonance Raman scattering spectra and 2D spatial intensity maps are recorded from thin Ag nanoparticle films coated with fatty acid Langmuir-Blodgett monolayers containing one-to-one binary mixtures, at varying concentrations, of two dye molecules of similar absorption and scattering cross section (n-pentyl-5-salicylimidoperylene and octadecylrhodamine B). The results reveal the change in the distribution of the two dyes within the monolayer, and the breakdown of ensemble spectral averaging, which occur as the single-molecule regime is approached. It is found that the unimolecular level is reached when 1-10 molecules of each dye occupy the 1-microm2 scattering areas probed by the laser. These signals are attributed to the rare spatial coincidence of isolated target analyte molecules and localized electromagnetic hot spots in the nanostructured metal film. The bianalyte nature of the samples provides strong corroborative support for the attribution of spectra to single molecules at high dilution, while the effect of domain formation/aggregation is found to be important at higher concentrations.