We address the question of sensitivity analysis for model outputs of any dimension using Regional Sensitivity Analysis (RSA). Classical RSA computes sensitivity indices related to the impact of model inputs variations on the occurrence of a target region of the model output space. In this work, we put this perspective one step further by proposing to find, for a given model input, the region whose occurrence is best explained by the variations of this input. When it exists, this region can be seen as a model behavior whose occurrence is particularly sensitive to the variations of the model input under study. We name this method mRSA (for maximized RSA). mRSA is formalized as an optimization problem using region-based sensitivity indices. Two formulations are studied, one theoretically and one numerically using a dedicated algorithm. Using a 2D test model and an environmental model producing time series, we show that mRSA, as a new model exploration tool, can provide interpretable insights on the sensitivity of model outputs of various dimensions.