In the context of ion acceleration driven by ultra-high contrast lasers using thin foils, there is a clear trend towards increasing ion energy when the target thickness is reduced. However when the target is too thin and the prepulse strength is not negligible, this trend is reversed due to degradation of the target mainly caused by prepulse-induced shocks, among other effects (thermal plasma expansion, early onset of transparency, etc.). In this paper, we propose and motivate the use of multi-layered targets for the purpose of enhancing the TNSA mechanism by means of attenuating the shock waves inside the target. It is demonstrated through hydrodynamic simulations that multi-layered targets, composed of alternating layers of plastic and gold, can significantly delay the time of shock wave breakout, reducing the shock energy that breaks out of the target and shortening the plasma scale-length. This approach paves the way for enhanced laser-driven ion acceleration using thinner targets even for relatively low contrast lasers.