Recently, large phase-change magnetoelectric response has been anticipated by a first-principles investigation of phases in the BiFeO3–BiCoO3 perovskite binary system, associated with the existence of a discontinuous morphotropic phase boundary (MPB) between multiferroic polymorphs of rhombohedral and tetragonal symmetries. This might be a general property of multiferroic phase instabilities, and a novel promising approach for room temperature magnetoelectricity. We review here our current investigations on the identification and study of additional material systems, alternative to BiFeO3–BiCoO3 that has only been obtained by high pressure synthesis. Three systems, whose phase diagrams were, in principle, liable to show multiferroic MPBs have been addressed: the BiMnO3–PbTiO3 and BiFeO3–PbTiO3 binary systems, and the BiFeO3–BiMnO3–PbTiO3 ternary one. A comprehensive study of multiferroism across different solid solutions was carried out based on electrical and magnetic characterizations, complemented with mechanical and electromechanical measurements. An in-depth structural analysis was also accomplished when necessary.