Constrained optimization problems are often characterized by multiple constraints that, in the practice, must be satisfied with different tolerance levels. Here, we evaluate the applicability of MAP-Elites to "illuminate" constrained search spaces by mapping them into feature spaces where each feature corresponds to a different constraint. We demonstrate the feasibility of this approach on a large set of benchmark problems, in various dimensionalities, and with different algorithmic configurations. As expected, numerical results show that a basic version of MAP-Elites cannot compete with state-of-the-art algorithms that use gradient information or constraint handling techniques. Nevertheless, it can find constraint violations vs. objectives trade-offs and thus provide new problem information. As such, it could be used in the future as an effective building-block for designing new constrained optimization algorithms.