  We show that any stochastically monotone Feller semigroup on $\mathbb{R}$ can
be extended by a consistent family of order-preserving Feller semigroups on the
successive powers of $\mathbb{R}$. We exhibit a specific such family, which is
uniquely characterized by a maximality property with respect to the
super-modular order on $\mathbb{R}$^n.
