  Generalized symmetrons are models that have qualitatively similar features to
the archetypal symmetron, but have barely been studied. In this article, we
investigate for what parameter values the fifth forces induced by disformally
coupling generalized symmetrons can provide an explanation for the difference
between baryonic and lens masses of galaxies. While it is known that the
standard symmetron struggles with providing an alternative source for the
lensing otherwise attributed to particle dark matter, we show that some
generalized symmetron models are more suitable for complying with existing
constraints on disformal couplings. This motivates future studies of these only
little explored models.
