Biclustering is the unsupervised learning task of mining a data matrix for submatrices, known as biclusters, with desirable properties. For instance, the goal can be to find groups of genes that are co-expressed under particular biological conditions. Many biclustering methods do not allow biclusters to overlap; others do, but need to specify how the biclusters interact at the overlapping regions. It is therefore of interest to devise methods that allow flexible, overlapping bicluster structures while not forcing the practitioner to specify bicluster interaction models. We propose a mixture modelling framework allowing biclusters to overlap but not requiring the practitioner to postulate any parameter interaction models between biclusters. Sharing a similar intuition to mixture-of-experts models, our model allows biclusters to specify partly overlapping regions of expertise in which the biclusters are able to model the data adequately. The uncertainty over assignments of data points to biclusters depends on the membership of data points to these regions of expertise. We perform inference and parameter estimation via a variational expectation-maximization framework. The model is easily adaptable to different data types and compares favorably to other approaches, both in a binary DNA copy number variation data set and in a miRNA expression data set.