I have Ubuntu 16.04.2 LTS, with kubuntu-desktop installed as well as ubuntu-gnome-desktop. The problem is that I cannot switch between Unity, Plasma, and Gnome. When I click the switcher, it does not show any desktop environments and defaults to Gnome. When I try to install Unity, which apparently has been uninstalled, it gives me a "you have held broken packages" error. The login is also quite broken, as it requires multiple tries to log in. In short, I might have irreversibly damaged my computer.
You can set a different default display manager using
sudo dpkg-reconfigure lightdm
(or gmd3, kdm, sddm, etc...)
Changing the default manager should work to restore the switcher functions. It seems lightdm does not like to play well with others.