  Testing gravity and the concordance model of cosmology, $\Lambda$CDM, at
large scales is a key goal of this decade's largest galaxy surveys. Here we
present a comparative study of dark matter power spectrum predictions from
different numerical codes in the context of three popular theories of gravity
that induce scale-independent modifications to the linear growth of structure:
nDGP, Cubic Galileon and K-mouflage. In particular, we compare the predictions
from full $N$-body simulations, two $N$-body codes with approximate time
integration schemes, a parametrised modified $N$-body implementation and the
analytic halo model reaction approach. We find the modification to the
$\Lambda$CDM spectrum is in $2\%$ agreement for $z\leq1$ and $k\leq 1~h/{\rm
Mpc}$ over all gravitational models and codes, in accordance with many previous
studies, indicating these modelling approaches are robust enough to be used in
forthcoming survey analyses under appropriate scale cuts. We further make
public the new code implementations presented, specifically the halo model
reaction K-mouflage implementation and the relativistic Cubic Galileon
implementation.
