Magnetoelectric materials that convert magnetic fields into electricity and vice versa are rare and usually complex, hard crystalline alloys. Recent work has shown that soft, highly deformable magnetoelectric materials may be created by using a strain-mediated mechanism. The electromagnetic and elastic deformation of such materials is intricately coupled, giving rise to a rather rich instability and bifurcation behavior that may limit or otherwise put bounds on the emergent magnetoelectric behavior. In this work, we investigate the magneto-electro-mechanical instability of a soft dielectric film subject to mechanical forces and external electric and magnetic fields. We explore the interplay between mechanical strain, electric voltage and magnetic fields and their impact on the maximum voltage and the stretch the dielectric material can reach. Specifically, we present physical insights to support the prospects to achieve wireless energy harvesting through remotely applied magnetic fields.