Hey there!
I don’t know much about quantile regression. It might be a good starting point to see what they do in this paper/package: https://www.jstatsoft.org/article/view/v076i07/v76i07.pdf
You can then try to translate their approach to Stan (or just their package).
You can also check out this thread or this thread for some examples of quantile regressions.
Hope this helps!
Cheers!
Max