We observe the appearance of multiple dipole surface plasmon resonances in spherical Ag nanoparticles when embedded in an organic semiconductor that exhibits a highly dispersive permittivity. Comparing the absorption spectra of thin-films with and without Ag nanoparticles reveals the presence of two plasmon peaks. Numerical simulations and calculations based on an electrostatic model allow us to attribute both peaks to dipole resonances, and show that the strong dispersion of the organic permittivity is responsible for this behavior. The presence of these two plasmon resonances was found to enhance the absorption of the organic semiconductor over a broad wavelength range.