  We show some new Wolstenholme type $q$-congruences for some classes of
multiple $q$-harmonic sums of arbitrary depth with strings of indices composed
of ones, twos and threes. Most of these results are $q$-extensions of the
corresponding congruences for ordinary multiple harmonic sums obtained by the
authors in a previous paper. Finally, we pose a conjecture concerning two kinds
of cyclic sums of multiple $q$-harmonic sums.
