I know that some docks support folders. Does Plank? If so, how can I add them?
Example image here:
Design from here.
Yes, Plank support folders for both apps and filesystem locations.
You can use Gnome-Pie as an alternative to grouping applications in the dock.
sudo add-apt-repository ppa:simonschneegans/testing
sudo apt-get update
sudo apt-get install gnome-pie
Video demonstration on Vimeo.