A multivariate linear regression model with q responses as a linear function of p independent variables is considered with a \(p\times q\) parameter matrix B. The least-squares or normal-theory maximum likelihood estimate of B is deficient in that it takes no account of the `across regression' correlations, and ignores the Stein effect. A remedy was offered by \textit{P. J. Brown} and \textit{J. V. Zidek} [Ann. Stat. 8, 64-74 (1980; Zbl 0425.62053)] in the form of a multivariate ridge estimator. A richer class of estimators is obtained here by casting the model in a linear hierarchical framework, obtaining the Brown and Zidek multivariate ridge estimates, \textit{B. Efron} and \textit{C. Morris}'s [Biometrika 59, 335-347 (1972; Zbl 0238.62072)] estimates of several normal mean vectors and \textit{T. Fearn}'s [ibid. 62, 89-100 (1975; Zbl 0297.62080)] Bayesian estimates of growth curves as special cases. The unknown covariance case results in an identifiability problem, which can be overcome by a Bayesian approach using conjugate priors for the unidentified covariance matrices.