  We study the problem of conformally deforming a manifold with boundary to
have vanishing {\sigma}4-curvature in the interior and constant H4- curvature
on the boundary. We prove that there are geometrically distinct solutions using
bifurcation results proven by Case, Moreira and Wang. Surprisingly, our
construction via products of a sphere and hyperbolic space only works for a
finite set of dimensions.
