Previous work shows that gene associations and network properties common between pairs of diseases can provide molecular evidence of comorbidity, but relationships among diseases may extend to larger groups. Formal concept analysis allows the study of multiple diseases based on a concept lattice whose structure indicates gene set commonality. We use the concept lattice for gene associations to evaluate the complexity of the relationships among diseases, and to identify concepts whose gene sets are candidates for further functional analysis. For this, we define a heuristic on the lattice structure that allows the identification of concepts whose gene sets indicate strong relationships among the included diseases, which are distinguished from other diseases in the family. Applying this approach to a family of renal diseases we demonstrate that this approach finds gene sets that may be promising for studying common (and differing) mechanism among a family of comorbid or phenotypically related diseases.