It has always been a disaster waiting to happen if you install multiple DE’s or WM’s together. It is possible though to have them installed altogether, and they will be accessible through your display manager whether its gdm, lightdm or any other login screen as stated by @elite
I find this a cooler way to have multiple DE’s without them having to overwrite or misconfigure something. While it will give you a few pains in the head to setup and get running, it is worth it.