# Is it possible to “add up” posterior distributions?

I've modeled a Bayesian mixed model where my outcome is count data (using a negative binomial model) in R using the rstanarm package. My data consists of multiple observations within sections of an organization on a monthly basis. Using the predict_posterior function, I have established a posterior distribution of fitted values for each observation section for each month.

Now, these sections are grouped into regions, and my client is interested in getting a yearly count in total for the entire organization and then broken down to yearly counts per regions and per sections. I could just add up the MAP estimates, but I want to keep the uncertainty around these estimates. My question is: Is it possible to add up each section's monthly posterior distributions? If so, how would one do this in R, given that each distribution consists of a vector of X draws?