Multiferroics, where (anti-) ferromagnetic, ferroelectric and ferroelastic order parameters coexist, enable manipulation of magnetic ordering by an electric field through switching of the electric polarization. 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. 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. 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.