  We analyse cosmological perturbations around a homogeneous and isotropic
background for scalar-tensor, vector-tensor and bimetric theories of gravity.
Building on previous results, we propose a unified view of the effective
parameters of all these theories. Based on this structure, we explore the
viable space of parameters for each family of models by imposing the absence of
ghosts and gradient instabilities. We then focus on the quasistatic regime and
confirm that all these theories can be approximated by the phenomenological
two-parameter model described by an effective Newton's constant and the
gravitational slip. Within the quasistatic regime we pinpoint signatures which
can distinguish between the broad classes of models (scalar-tensor,
vector-tensor or bimetric). Finally, we present the equations of motion for our
unified approach in such a way that they can be implemented in
Einstein-Boltzmann solvers.
