What kind of difficulty you see?
I find that sometimes it might be easier to approximate the posterior with a Gaussian for the next batch of updating, eg see Performance speedup for updating posterior with new data and code here: https://github.com/junpenglao/Planet_Sakaar_Data_Science/blob/master/PyMC3QnA/Update%20prior%20with%20Interpolation.ipynb (see last cell)
If you have bounded variables, it would be a bit more difficult as you need to work out the inverse projection from unconstrained parameter space back to the bounded space.