  We consider the propagation of totally symmetric bosonic fields on generic
background spacetimes. The mutual compatibility of the dynamical equations and
constraints severely constrains the set of geometries where consistent
propagation is possible. To enlarge this set in this article we allow several
background fields to be turned on. We were able to show that massive fields of
spin s greater than or equal to three may consistently propagate in a large set
of non-trivial spacetimes, such as asymptotically de-Sitter, flat and
anti-de-Sitter black holes geometries, as long as certain conditions between
the various background fields are met. For the special case of massive spin-2
fields the set of allowed spacetimes is larger and includes domain-wall-type
geometries, such as the Freedman-Robertson-Walker metric. We comment on the
assumptions underlying our study and on possible applications of our results.
