A general theory for microstructure in systems of copolymers with strongly interacting groups (SIGs) is proposed. The so-called superstrong segregation limit, corresponding to rather short blocks containing SIGs and strong attraction between them, is considered in detail. In particular, multiplet formation in melts and solutions of ionomers (block ionomers) is studied : It is shown that as the interaction parameter increases, the most stable shape of a multiplet continuously changes from spherical to disklike (oblate ellipsoid). A further increase of the interaction parameter induces another (first order) transition from disklike multiplets to lamellae. The same transitions could be induced by decreasing the average length of ionic blocks in block ionomer systems. The relevant experimental observations are discussed.