Predicting distributional parameters with prediction of mean?

In brms, can the same posterior distribution of parameters be used to predict the distribution’s mean but also another parameter (like sigma or shape) with some linear transform (prior to the link)? For example, say I want to model some data with a gamma distribution whose shape parameter linearly (before the link) decreases with the predicted mean. If so, what would the syntax be or please point me to the relevant part of the help file if I have missed it?