MRPP or alike function on non-metric dissimilarity matrix

Dear All,

I would like to test the separation of groups of observations based on a
dissimilarity matrix but the dissimilarity matrix is strongly non-metric. I
thought of MRPP (multi-response permutation procedure) but I don't know if
it requires (semi-)metric dissimilarity matrix or not. Could you recommend
a better solution?
I would appreciate your help.
Best regards,

Attila