It's not possible to control the specific type of points that are plotted. Apple could add/remove/change the specific types it displays in any future update of Map Kit. As you mentioned, your only course of action is setting showsPointsOfInterest
.
You could use a third-party place database from Foursquare or Facebook to get similar points of interest and plot them on your map, however there is no guarantee that the results would match the ones Apple would otherwise show.