Multiferroics, where (anti-) ferromagnetic, ferroelectric and ferroelastic order parameters coexist(1-5), enable manipulation of magnetic ordering by an electric field through switching of the electric polarization(6-9). It has been shown that realization of magnetoelectric coupling in a single-phase multiferroic such as BiFeO(3) requires ferroelastic (71 degrees, 109 degrees) rather than ferroelectric (180 degrees) domain switching(6). However, the control of such ferroelastic switching in a single-phase system has been a significant challenge as elastic interactions tend to destabilize small switched volumes, resulting in subsequent ferroelastic back-switching at zero electric field, and thus the disappearance of non-volatile information storage(10,11). Guided by our phase-field simulations, here we report an approach to stabilize ferroelastic switching by eliminating the stress-induced instability responsible for back-switching using isolated monodomain BiFeO(3) islands. This work demonstrates a critical step to control and use non-volatile magnetoelectric coupling at the nanoscale. Beyond magnetoelectric coupling, it provides a framework for exploring a route to control multiple order parameters coupled to ferroelastic order in other low-symmetry materials.