What is the nonparametric variant of multivariate ANOVA with more than one one factor (and with interactions between factors)?

Question

I analyze real data where assuptions of classical multiway (more than one factor assumed) MANOVA (more than one response variable) are not met (normality, equal variances). Is there any nonparametric variant? Note that Friedman test in only alternative to repeated measures ANOVA, not to more general multiway MANOVA with interactions.