We revisit the problem of building consistent interactions for a multiplet of partially massless spin-2 fields
in (anti-)de Sitter space. After rederiving and strengthening the existing no-go result on the impossibility of
Yang-Mills type non-abelian deformations of the partially massless gauge algebra, we prove the uniqueness
of the cubic interaction vertex and field-dependent gauge transformation that generalize the structures known
from single-field analyses. Unlike in the case of one partially massless field, however, we show that for two or
more particle species the cubic deformations can be made consistent at the complete non-linear level, albeit
at the expense of allowing for negative relative signs between kinetic terms, making our new theory akin to
conformal gravity. Our construction thus provides the first example of an interacting theory containing only
partially massless fields.
