We theoretically study the power spectra of a microcavity–quantum dot system under incoherent pumping of photons and excitons, considering two models: one with linked cavity loss rate and pumping, and one with independent cavity loss rate and pumping. We investigate the transition from strong to weak coupling under low and high incoherent pumping in each model and determine sets of parameters necessary to achieve these regimes of light–matter interaction. Despite their differences, both models exhibit a sequence of transitions between weak, strong, and weak coupling as the pumping is increased. This prediction has not yet been observed.