This paper introduces a mechanism design approach that allows dealing with the multiple equilibrium problem, using mechanisms that are robust to bounded rationality. This approach is a tool for constructing supermodular mechanisms, i.e., mechanisms that induce games with strategic complementarities. In quasilinear environments, I prove that if a social choice function can be implemented by a mechanism that generates bounded strategic substitutes—as opposed to strategic complementarities—then this mechanism can be converted into a supermodular mechanism that implements the social choice function. If the social choice function also satisfies some efficiency criterion, then it admits a supermodular mechanism that balances the budget. Building on these results, I address the multiple equilibrium problem. I provide sufficient conditions for a social choice function to be implementable with a supermodular mechanism whose equilibria are contained in the smallest interval among all supermodular mechanisms. This is followed by conditions for supermodular implementability in unique equilibrium. Finally, I provide a revelation principle for supermodular implementation in environments with general preferences.