Hi!
I’m not 100% sure what you mean. You can of have any number of dimensions you like in an observed data. For example, here is an example of using the broadcasting rules to fit a stack of independent regressions all at the same time. Or here is a general example showing how to fit data with a Multivariate Normal.
It would be useful if you could post a little bit more about your model. Do you have a generative model (in math, I mean) that you could share, or a minimal pymc or numpy code snippet showing how you would generate artificial data? Either of these would help clarify your question.