  We perform a complete classification of the consistent two-derivative cubic
couplings for a system containing an arbitrary number of massless spin-1,
massless spin-2, and partially massless (PM) spin-2 fields in $D$-dimensional
(anti-)de Sitter space. In addition to previously known results, we find a
unique candidate mixing between spin-1 and PM spin-2 fields. We derive all the
quadratic constraints on the structure constants of the theory, allowing for
relative ``wrong-sign'' kinetic terms for any of the fields. In the particular
case when the kinetic terms in each sector have no relative signs, we find that
the unique consistent non-trivial theory is given by multiple independent
copies of conformal gravity coupled to a Yang-Mills sector in $D=4$. Our
results strengthen the well-known no-go theorems on the absence of mutual
interactions for massless and PM spin-2 fields.
