As i have been playing on kitpvp, i have seen many teams. You should be able to write / team create or something along those lines. This is just a suggestion but i still think that you should add it for teams not to hit each other.
No support: - Explain more or give us more information about your idea? - This would be too overpowered. - Should be a apart gamemode, like @iShadinq_ said.
I feel like this would be a amazing idea if there was a Limit to the "Teams in KitPvP", I do agree what other people say it would be too OP but if there was a limit I would Support No Support :P