However, when multiple excitation manifolds are accessible, the effects of cavity loss become more complicated, as demonstrated by the work shown in Fig. (adapted from Ref. 303). The potential energy surfaces considered (Fig. )) in this model of MgH+ coupled to a cavity span states with different numbers of excitations, including doubly excited states composed of a molecular excitation and a photonic excitation (states |1, A⟩ and |1, B⟩) or two photonic excitations (state |2, X⟩). These doubly excited states can undergo cavity loss (indicated by downward arrows) and incoherently transfer population to the singly excited manifold. The combination of these loss channels along with the multiple cavity-induced avoided crossings leads to non-monotonic effects when the cavity loss rate or light-matter coupling strength are varied. The remaining non-dissociated population after photoexcitation (Fig. (ii)) was found to be smaller with a cavity lifetime of 10 fs than with a cavity lifetime of 1 fs or 1000 fs. The remaining population did generally increase with larger electric field strength, but this was not always the case since there are multiple local maxima and minima in the remaining population for longer lifetimes above 1000 fs. These nuanced, non-monotonic features highlight the importance of using detailed theoretical calculations to predict the optimal cavity parameters for controlling photochemical reactions.