You will have to do this in three solves. One for each type of facility you want to find. So set up a CF layer with the incidents (block centroids) and then load in the first type of facilities and solve for 1 closest. Export the results. Then, unload/remove the facilities and load in the next set and solve for 1 closest and export. Repeat for the third set. Alternatively you can create the CF layer with the incidents and copy this layer twice. Now you have three layers. Load each set of demand points to them and solve for 1 closest and export/merge the results.