  We revisit a particular ghost-free bimetric model which is related to both
partial masslessness (PM) and conformal gravity. Linearly, the model propagates
six instead of seven degrees of freedom not only around de Sitter but also
around flat spacetime. Nonlinearly, the equations of motion can be recast in
the form of expansions in powers of curvatures, and exhibit a remarkable amount
of structure. In this form, the equations are shown to be invariant under
scalar gauge transformations, at least up to six orders in derivatives, the
lowest order term being a Weyl scaling of the metrics. The terms at
two-derivative order reproduce the usual PM gauge transformations on de Sitter
backgrounds. At the four-derivative order, a potential obstruction that could
destroy the symmetry is shown to vanish. This in turn guarantees the gauge
invariance to at least six-orders in derivatives. This is equivalent to adding
up to 10-derivative corrections to conformal gravity. More generally, we
outline a procedure for constructing the gauge transformations order by order
as an expansion in derivatives and comment on the validity and limitations of
the procedure. We also discuss recent arguments against the existence of a PM
gauge symmetry in bimetric theory and show that, at least in their present
form, they are evaded by the model considered here. Finally, we argue that a
bimetric approach to PM theory is more promising than one based on the
existence of a fundamental PM field.
