Seemingly unrelated regression (SUR) models are useful in studying the interactions among economic variables. In a high dimensional setting or when applied to large panel of time series, these models require a large number of parameters to be estimated and suffer of inferential problems. To avoid overparametrization and overfitting issues, we propose a hierarchical Dirichlet process prior for SUR models, which allows shrinkage of SUR coefficients toward multiple locations and identification of group of coefficients. We propose a two-stage hierarchical prior distribution, where the first stage of the hierarchy consists in a lasso conditionally independent prior distribution of the Normal-Gamma family for the SUR coefficients. The second stage is given by a random mixture distribution for the Normal-Gamma hyperparameters, which allows for parameter parsimony through two components: the first one is a random Dirac point-mass distribution, which induces sparsity in the SUR coefficients; the second is a Dirichlet process prior, which allows for clustering of the SUR coefficients.