We present a novel extension of the celebrated composite quantile regression (CQR) method proposed by Zou and Yuan (2008) to handle multiple-output cases. Building upon the concept of multivariate quantiles introduced by Chernozhukov et al. (2017) and Hallin et al. (2021), we generalize the univariate CQR estimator. We show that the univariate CQR estimator can be formulated as an optimal transport problem, and this formulation naturally extends to the multivariate case. We establish the consistency of the proposed estimator and provide the rate of convergence. Additionally, we highlight the robustness of our method by showing that it remains valid even when the random errors follow heavy-tail distributions or when the support of the random errors is non-convex. To validate our findings, we conduct comprehensive simulations that illustrate the effectiveness of the proposed approach.