Co-clustering can be viewed as a two-way (bilinear) factorization of a large data matrix into dense/uniform and possibly overlapping sub-matrix factors (co-clusters). This combinatorially complex problem emerges in several applications, including behavior inference tasks encountered with social networks. Existing co-clustering schemes do not exploit the fact that overlapping factors are often sparse, meaning that their dimension is considerably smaller than that of the data matrix. Based on plaid models which allow for overlapping submatrices, the present paper develops a sparsity-cognizant overlapping co-clustering (SOC) approach. Numerical tests demonstrate the ability of the novel SOC scheme to globally detect multiple overlapping co-clusters, outperforming the original plaid model algorithms which rely on greedy search and ignore sparsity.