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 LixWO3 and NaxWO3.