you could alternatively conduct a pairwise Mann-Whitney (=Wilcoxon) Test
with Bonferroni-Holms correction, but I don't know, if this would help.
Dunn test is known as a conservative one.
If you have comparisons, which would allow a stepwise testing (you need to
expect an increase/decrease of values in ascending order; e.g. dose
response) you could conduct Jonckheere test.
The first thing, which I would try, is to get normal distributed data by
means of transformation and then conduct parametric tests (e.g. Dunnett's t-
test). Only if you can't reach normality and homogenity of variances
conduct nonparametric tests.
I'm just a biologist, who knows only little about statistics. I'm also
looking for a powerful nonparametric multiple comparison test and have not
found one yet. It would be great, if a professional statistican could give