The control of the magnetization of a material with an electric field would make the design and the integration of novel electronic devices possible. This explains the renewed interest in multiferroic materials. Progress in this field is currently hampered by the scarcity of the materials available and the smallness of the magnetoelectric effects. Here we present a proof-of-principle experiment showing that engineering large strains through nanoscale size reduction is an efficient route for increasing magnetoelectric coefficients by orders of magnitude. The archetype magnetoelectric material, Cr2O3, in the form of epitaxial clusters, exhibits an unprecedented 600% change in magnetization magnitude under 1 V. Furthermore, a multiferroic phase, with both magnetic and electric spontaneous polarizations, is found in the clusters, while absent in the bulk.