In the present work, we investigate the modified nonlinear pump-probe optical properties due to the excitonic–plasmonic interaction of a double semiconductor quantum dot (SQD) molecule coupled to a metal nanoparticle (MNP). More specifically, we study the absorption and the dispersion spectra of a weak electromagnetic field in a hybrid structure with two counterparts, a molecule of two coupled SQDs, and a spherical MNP driven by a field of high intensity. We solve the relevant density matrix equations, calculate the first-order optical susceptibility of the probe field in the strong pumping regime, and investigate the way in which the distance between the two counterparts modifies the optical response, for a variety of values of the physical constants of the system, including the pump-field detuning, the tunnelling rate, and the energy separation gap associated with the excited states of the coupled SQDs.