We theoretically investigate the multipolar effects on the dipole-forbidden transitions of a semiconductor quantum dot. An approximated expression for the decay rate of these transitions is derived. Unlike the general theory of the spontaneous emission beyond the dipole approximation, the distinct roles of the emitter and the vacuum electric field in the transition rate are here clearly recognizable and can be separately optimized. We illustrate the potential of this formalism by calculating the spontaneous emission decay rate of an InAs/GaAs quantum dot embedded into two realistic nanostructures—an L3 photonic crystal cavity and a plasmonic dimer antenna. The obtained results show that, although the two structures provide an enhancement of the same order of magnitude, the plasmonic antenna constitutes a more promising candidate for the experimental observation of the dipole-forbidden transitions of a quantum dot.