Employing an elastic lattice gas (LG) model we investigate the intercalation of ions into a host material, undergoing a sequence of structural transformations (monoclinic→tetragonal→cubic). It is shown that an effective potential for the ions results from the intercalation-induced restructuring of the host. This interaction induces distinct peaks (one is sharp, while the other is broad) in the current–concentration diagram. The sharp peak signals a droplet formation around the domain walls separating the host domains of different symmetry (monoclinic→tetragonal). The broad peak may be associated with a continuous (order–disorder) transition (tetragonal→cubic). Theoretical results agree well with experimental data for Li x WO3 and Na x WO3.