We propose and justify by the finite-difference time-domain method an efficient strategy to enhance the spontaneous emission of a fluorophore with a multi-resonance plasmonic antenna. The custom-designed asymmetrical antenna consists of two plasmonic nanoparticles with different sizes and is able to couple efficiently to free space light through multiple localized surface plasmon resonances. This design simultaneously permits a large near-field excitation near the antenna as well as a high quantum efficiency, which results in an unusual and significant enhancement of the fluorescence of a single emitter. Such an asymmetrical antenna presents intrinsic advantages over single particle or dimer based antennas made using two identical nanostructures. This promising concept can be exploited in the large domain of light-matter interaction processes involving multiple frequencies.