  In this work we consider a cosmological model in which dark energy is
portrayed by a canonical scalar field which is allowed to couple to the other
species by means of a disformal transformation of the metric. We revisit the
current literature by assuming that the disformal function in the metric
transformation can depend both on the scalar field itself and on its
derivatives, encapsulating a wide variety of scalar-tensor theories. This
generalisation also leads to new and richer phenomenology, explaining some of
the features found in previously studied models. We present the background
equations and perform a detailed dynamical analysis, from where new disformal
fixed points emerge, that translate into novel cosmological features. These
include early scaling regimes between the coupled species and broader stability
parameter regions. However, viable cosmological models seem to have suppressed
disformal late-time contributions.
