In this article we develop a methodology for the joint value added analysis of multiple outcomes that takes into account the inherent correlation between them. This is especially crucial in the analysis of higher education institutions. We use a unique Colombian database on universities, which contains scores in five domains tested in a standardized exit examination that is compulsory in order to graduate. We develop a new estimation procedure that accommodates any number of outcomes. Another novelty of our method is related to the structure of the random effect covariance matrix. Effects of the same school can be correlated and this correlation is allowed to vary among schools.