We use conformal, but ghostful, Weyl gravity to study its ghost-free, second
derivative, partially massless (PM) spin 2 component in presence of Einstein gravity with
positive cosmological constant. Specifically, we consider both gravitational- and self-
interactions of PM via the fully non-linear factorization of conformal gravity's Bach
tensor into Einstein times Schouten operators. We find that extending PM beyond linear
order suffers from familiar higher-spin consistency obstructions: it propagates only in
Einstein backgrounds, and the conformal gravity route generates only the usual safe,
Noether, cubic order vertices.