  The variety of magnetic phases observed in rare-earth heterostructures at low
temperatures \cite{Jehan}, such as Ho/Y, may be elucidated by an ANNNI-like
model Hamiltonian. In previous work modelling bulk Ho \cite{Seno}, such a
Hamiltonian with a one-dimensional parameter space produced a single multiphase
point. In contrast, the parameter space of the heterostructure model is
three-dimensional, and instead of an isolated multiphase point, we find
two-dimensional multiphase regions. In an example of Villain's ``order from
disorder'' \cite{Villain80a,Villain91}, an infinitesimal temperature breaks the
ground-state degeneracy. In first order of a low-temperature expansion, we find
that the degeneracy is broken everywhere in a multiphase region except on a
line. A segment of the line appears to remain multiphase to all orders in a
low-temperature expansion when the number $L$ of magnetic layers between
non-magnetic spacers is 4 but not for other values of $L$. For L=4, the
hierarchy of phases more closely resembles that in the ANNNI model than in the
bulk six-state clock model on which the present model is based.
