  We show that the multivariate additive higher Chow groups of a smooth affine
$k$-scheme $\Spec (R)$ essentially of finite type over a perfect field $k$ of
characteristic $\not = 2$ form a differential graded module over the big de
Rham-Witt complex $\W_m\Omega^{\bullet}_{R}$. In the univariate case, we show
that additive higher Chow groups of $\Spec (R)$ form a Witt-complex over $R$.
We use these structures to prove an \'etale descent for multivariate additive
higher Chow groups.
