  Ghost-free bimetric theories describe nonlinear interactions of massive and
massless spin-2 fields and, hence, provide a natural framework for
investigating the phenomenon of partial masslessness for massive spin-2 fields
at the nonlinear level. In this paper we analyze the spectrum of the ghost-free
bimetric theory in arbitrary dimensions. Using a recently proposed
construction, we identify the candidate nonlinear partially massless (PM)
theories. It is shown that, in a 2-derivative setup, nonlinear PM theories can
exist only in 3 and 4 dimensions. But on adding Lanczos-Lovelock terms to the
bimetric action it is found that higher derivative nonlinear PM theories also
exist in higher dimensions. This is consistent with existing results on the
direct construction of cubic vertices with PM gauge symmetry. We obtain the
candidate nonlinear PM theories in 5, 6 and 8 dimensions but show that none
exist in 7 dimensions.
