The traditional rank-based tests are limited in the designs they can address.  Kruskal–Wallis is analogous to a one-way anova, and Friedman and Quade handle unreplicated complete block design.

Permutation tests should probably replace all the rank-based tests.  The coin package in R is pretty flexible, but I think the most complex design it handles is a one-way anova with blocks, though it also allows multiple dependent variables, and different types of dependent or independent variables.

For potential approaches for two-way analyses, see:

https://journal.r-project.org/archive/2016-1/feys.pdf