We propose a new Bayesian parametric model for integrative, unsupervised clustering across data sources. Such approaches are important in disease subtyping. In our method, we cluster samples in relation to each data source, distinguishing it from methods like Cluster of Cluster Assignments and iCluster, but cluster labels have across-dataset meaning, allowing cluster information to be shared between data sources. We propose a two-way latent structure of cluster assignment variables, within each dataset and across datasets (per sample), which allows borrowing strength across data sources. Importantly, a common scaling across data sources is not required. Inference is obtained by a Gibbs Sampler, which we improve to better cope with sparsity of unoccupied clusters and speed of convergence, and fit models with Gaussian and more general densities which influences across-dataset cluster label sharing. Uniquely, our formulation makes no nestedness assumptions of samples across data sources. We apply our model to a Norwegian breast cancer cohort of ductal carcinoma in-situ and invasive tumors, comprised of somatic copy-number alteration, methylation and expression datasets. We find enrichment in the Her2 subtype and ductal carcinoma among those observations exhibiting greater cluster correspondence across expression and CNA data.