  The perturbative treatment of dark matter in structure formation relies on
the existence of a well-defined expansion parameter, $k/k_{\rm NL}$, with
$k_{\rm NL}$ signalling the onset and ultimately the leading role of
non-linearities in the system. Cosmologies beyond the {\Lambda}CDM model often
come with additional degree(s) of freedom. The scale $k_{\rm V}$ at which
non-linearities become important in the additional sector(s) can be rather
different from $k_{\rm NL}$. For theories endowed with a Vainshtein-type
screening mechanism, $k_{\rm V}$ sets the scale where screening becomes
efficient and restores continuity with the predictions of general relativity.
This is precisely the dynamics that allows such theories to pass existing
observational tests at scales where general relativity has been tested with
exquisite precision (e.g. solar system scales). We consider here the
mildly-non-linear scales of a dark matter component coupled to a galileon-type
field and focus in particular on the case of a $k_{\rm V}$ < $k_{\rm NL}$
hierarchy. We put forward a phenomenological framework that describes the
effects of screening dynamics on large scale structure observables.
