Gold crescent-shaped nanoparticles, exhibiting multiple resonances in the visible and near-infrared spectral region, were characterized in terms of their optical response to thin dielectric coatings. A strong red shift of the resonances is observed upon the addition of material. The coating thickness at which saturation of the shift sets in is resonance dependent and is directly connected to the spatial extension of the near field associated to each of the plasmonic modes, which is estimated through simplified theoretical models. These structures are advantageous for sensing for two reasons. First, the small modal volume makes them selectively sensitive to the first 10-30 nm distance from the gold. Second, each mode yields independent information about the coating and therefore in principle allows the determination of more than one free parameter of the coating, for example, thickness and refractive index.