  A pair of complex-conjugate fixed points that lie close to the real axis
generates a large mass hierarchy in the real renormalization group flow that
passes in between them. We show that pairs of complex fixed points that are
close to the real axis and to one another generate multiple hierarchies, some
of which can be parametrically enhanced. We illustrate this effect at weak
coupling with field-theory examples, and at strong coupling using holography.
We also construct complex flows between complex fixed points, including flows
that violate the $c$-theorem.
