Is it possible to play team deathmatch or clan arena with more than two teams?
Unfortunately, it doesn't seem like Quake Live allows more than two teams to participate in those two gamemodes.
I did some research on the modding communities built around Quake Live and have not come up with any results pertaining to allowing a higher quantity of participating teams.
Good luck in case you find extra information regarding it. If I've made a mistake with the information I've provided, please let me know and I'll fix it or remove it.