We use optical and scanning force microscopy to explore the possibility of switching the stability of a bilayer of poly(methyl methacrylate) (PMMA) on polystyrene by simply changing the film thickness. We show that for thin PMMA layers on thicker polystyrene films the PMMA layer is unstable to thickness fluctuations. However, polystyrene layers are unstable when they are substantially thinner than the now stable PMMA film. Dewetting morphologies are cataloged as a function of the thickness of individual polymer layers by identifying which layer is unstable by which mechanism, be it spinodal dewetting or heterogeneous thermal nucleation. Our results are in good agreement with a linear stability analysis of the influence of long-range dispersion forces, but also indicate the influence of film preparation and small variations of material properties.