Modelling multiple correlated variables

I have a follow-up PYMC3 question. What would I have to do in case I want to set the correlation between variables when variables are not all normal but a mixture of different kinds of distributions? In that case, it would not be appropriate to use a multivariate normal distribution (pm.MvNormal), as it only generates normal distributions. I am wondering if there is something like a multivariate distribution that can output different kind of distributions? I would like to do something similar to what is possible with Crystal Ball where it is possible to correlate different input variables having different distributions → https://www.oracle.com/docs/tech/middleware/correlated-assumptions.pdf