  We study the possibility for a unitary theory of partially-massless (PM)
spin-two field interacting with Gravity in arbitrary dimensions. We show that
the gauge and parity invariant interaction of PM spin two particles requires
the inclusion of specific massive spin-two fields and leads to a reconstruction
of Conformal Gravity, or multiple copies of the latter in even dimensions. By
relaxing the parity invariance, we find a possibility of a unitary theory in
four dimensions, but this theory cannot be constructed in the standard
formulation, due to the absence of the parity-odd cubic vertex therein.
Finally, by relaxing the general covariance, we show that a `non-geometric'
coupling between massless and PM spin-two fields may lead to an alternative
possibility of a unitary theory. We also clarify some aspects of interactions
between massless, partially-massless and massive fields, and resolve
disagreements in the literature.
