# permutation testing and mixed effects models

I am rather new to both permutation tests and mixed effects models, so forgive me if this is a ridiculous question. I would like to run a permutation test for a model that has a random effect, although I am not interested in the random effect, just a fixed effect. I realize that for a standard permutation test one simply permutes the outcome. However, can one do this when there are random effects? Instinctively I would say yes, but my instincts often prove wrong! Thank you!