  We address the issue of the all order multiplicative renormalizability of
$SU(2)$ Gribov-Zwanziger theories quantized in the maximal Abelian gauge in
presence of confined matter fields. The non-linear character of the maximal
Abelian gauge requires the introduction of quartic interaction terms in the
Faddeev-Popov ghosts as well as in the localizing Zwanziger fields, extended a
well known feature of this gauge. We show that, when scalar matter fields are
introduced, a second quartic interaction term between scalar fields,
Faddeev-Popov ghosts and Zwanziger-like fields naturally arises. A BRST
invariant action accounting for those quartic interaction terms is identified
and proven to be multiplicative renormalizable to all orders by means of the
algebraic renormalization procedure.
