The modified Box-Meyer method (MBMM) has been proposed to identify active factors in an unreplicated screening experiment. This work aims to introduce the MBMM into the analysis of a screening experiment with multivariate responses. We propose an empirical Bayes approach to estimate the hyper-parameters instead of integrating them out. By doing so, the computational complexity is reduced. We illustrate the proposed approach by analyzing an examples, the dyestuffs experiment and all the active factors are identified successfully.