Correlated variables or variable with correlated dimensions?

Hello, I am setting up an inference problem where I have about a dozen (lets say N) variables and each variable has 3 properties. Each property has a uniform prior with different bounds.

Until now I have been setting the problem up by defining Nx3 independent variables with uniform priors. But actually for each variable the three properties are highly correlated.

I came across several examples that deal with correlated variables (1, 2, 3, 4) but none actually addresses uniform priors. It seems like the pm.MvNormal distribution with an appropriate correlation matrix would do the job, but in my case the variables are not normally distributed.

Is there a simpler way to accomplish this, for example to assign correlation between the dimensions of a variable? From what I got, when assigning dimensions, these are still independent.

Thank you for the help,