  The $\texttt{Hi-COLA}$ code is an efficient dark matter simulation suite that
flexibly handles the Horndeski family of modified gravity models. In this work
we extend the scope of $\texttt{Hi-COLA}$ to accommodate Horndeski theories
with K-mouflage screening, allowing for the computation of matter power spectra
in the non-linear regime in these models. We explore the boost of the dark
matter power spectrum relative to GR-$\Lambda$CDM in K-mouflage gravity, and
also discuss how large-scale structure computations change between the Einstein
and Jordan frames. A dissection of the relative contributions of the modified
background, linear growth, fifth force, and the conformal factor (a new
inclusion to $\texttt{Hi-COLA}$) to the boost factor is presented. The ability
of $\texttt{Hi-COLA}$ to run with general Horndeski models and multiple
screening mechanisms makes it an ideal tool for testing gravity with upcoming
galaxy survey data.
