We investigated the dependence of the dewetting velocity of a thin, low-viscosity polystyrene (PS) top film on a poly(methyl methacrylate) (PMMA) double layer consisting of a low-viscosity underlayer of thickness h(L) coated with a high-viscosity middle layer of thickness h(M). The addition of the liquid underlayer generated complex nonmonotonic behavior of the dewetting velocity as a function of increasing h(M). In particular, we observed an acceleration of dewetting for an intermediate range of h(M). This phenomenon has been interpreted by a combination deformation of the middle elastic layer and a concurrent change in the contact angle. On one hand, deformation led to the formation of a trench that dissipated energy during its movement through the liquid underlayer and thus caused a slowing down of dewetting. However, with an increase in the thickness of the elastic middle layer, the size of the trench decreased and its influence on the dewetting velocity also decreased. On the other hand, the deformation of the elastic layer also led to an increase in the contact angle. This increase in the driving capillary forces caused an increase in the dewetting velocity.