A promising approach for obtaining large magnetoelectric response at room temperature in single-phase materials is to make use of phase-change phenomena at structural instabilities of a multiferroic state. This is the case of perovskites showing morphotropic phase boundary (MPB) between ferroelectric polymorphs with differentiated magnetic orderings, like in BiFeO3-PbTiO3. Indeed, distinctive magnetoelectric effects were recently shown in Mn-modified BiFeO3-PbTiO3, associated with the electric field induced phase transition between the coexisting MPB phases. We report here analogous effects under the magnetic field in 0.7BiFeO3-0.3PbTiO3 that shed light into the reversibility of the phase-change phenomena, and the role of the magnetic ordering in the phase coexistence at the structural instability characteristic of the MPB.Results demonstrate magnetic field driven phase-change phenomena.