We show that, whenever $\Gamma$ is a countable abelian group and $\Delta$ is a finitely-generated subgroup of $\Gamma$, a generic measure-preserving action of $\Delta$ on a standard atomless probability space $(X,\mu )$ extends to a free measure-preserving action of $\Gamma$ on $(X,\mu )$. This extends a result of Ageev, corresponding to the case when $\Delta$ is infinite cyclic.