  This paper is concerned with theories of gravity that contain a scalar
coupled both conformally and disformally to matter through the metric. By
systematically deriving the non-relativistic limit, it is shown that no new
non-linear screening mechanisms are present beyond the Vainshtein mechanism and
chameleon-like screening. If one includes the cosmological expansion of the
universe, disformal effects that are usually taken to be absent can be present
in the solar system. When the conformal factor is absent, fifth-forces can be
screened on all scales when the cosmological field is slowly-rolling. We
investigate the cosmology of these models and use local tests of gravity to
place new constraints on the disformal coupling and find
$\mathcal{M}>\mathcal{O}(\textrm{eV})$, which is not competitive with
laboratory tests. Finally, we discuss the future prospects for testing these
theories and the implications for other theories of modified gravity. In
particular, the Vainshtein radius of solar system objects can be altered from
the static prediction when cosmological time-derivatives are non-negligible.
