We give a new proof of a theorem of Farb and Handel stating that when n is at least 4, every isomorphism between finite-index subgroups of $Out(F_n)$ extends to an inner automorphism of $Out(F_n)$. Our proof enables us to extend their theorem to the case where n=3. More generally, we prove that several interesting normal subgroups of $Out(F_n)$, such as the Torelli subgroup $IA_n$, have $Out(F_n)$ as their abstract commensurator. This is a joint work with Ric Wade.