  We show that higher spin systems specific to cosmological spaces are subject
to the same problems as models with Poincar'e limits. In particular, we analyse
partially massless (PM) spin 2 and find that both its gravitational coupling
and nonlinear extensions suffer from the usual [background- and self-coupling]
difficulties: Consistent free field propagation does not extend beyond
background Einstein geometries. Then, using conformal Weyl gravity (CG), which
consists of relative ghost PM and graviton excitations, we find that avoiding
graviton-ghosts restricts CG-generated PM self-couplings to the usual, safe,
Noether current cubic ones.
