  Epitaxial films which contains more than one crystallographic orientation are
of interest due to the possibility of altered magnetic, electrical, and optical
properties. Thin films of FeSe have been grown on single-crystal MgO substrates
under conditions that produces the simultaneous, epitaxial growth of tetragonal
and hexagonal phases. We show that this double epitaxy is characterized by
phase domains with a well-defined epitaxial relationship to each other and that
the relative phase fraction can be controlled. For growth temperatures of
350-450 degrees C, the (001)-oriented tetragonal phase (${\beta}$-FeSe) grows
with its unit cell aligned with the cubic substrate, while a (101)-oriented
hexagonal phase (Fe$_7$Se$_8$) shows domains with two different in-plane
orientations separated by 45 degrees. Additionally, the ${\beta}$-FeSe phase
can be chosen to be (001)- or (101)-oriented with respect to the substrate,
with the (101) orientation containing three rotated domains.
