  Let $f: (X,D) \to B$ be a stably family with log canonical general fiber. We
prove that, after a birational modification of the base $\tilde{B} \to B$,
there is a morphism from a high fibered power of the family to a pair of log
general type. If in addition the general fiber is openly canonical, then there
is a morphism from a high fibered power of the original family to a pair openly
of log general type.
