Magnetostrictive materials transduce magnetic and mechanical energies and when combined with piezoelectric elements, evoke magnetoelectric transduction for high-sensitivity magnetic field sensors and energy-efficient beyond-CMOS technologies. The dearth of ductile, rare-earth-free materials with high magnetostrictive coefficients motivates the discovery of superior materials. Fe_1-xGa_x alloys are amongst the highest performing rare-earth-free magnetostrictive materials; however, magnetostriction becomes sharply suppressed beyond x = 19% due to the formation of a parasitic ordered intermetallic phase. Here, we harness epitaxy to extend the stability of the BCC Fe_1-xGa_x alloy to gallium compositions as high as x = 30% and in so doing dramatically boost the magnetostriction by as much as 10x relative to the bulk and 2x larger than canonical rare-earth based magnetostrictors. A Fe_1-xGa_x - [Pb(Mg_1/3Nb_2/3)O₃]_0.7-[PbTiO₃]_0.3 (PMN-PT) composite magnetoelectric shows robust 90° electrical switching of magnetic anisotropy and a converse magnetoelectric coefficient of 2.0 × 10^-5 s m^-1. When optimally scaled, this high coefficient implies stable switching at ~80 aJ per bit.