I like this idea but you'd have to be very careful about how you do it. I would strongly advise against doing CTF multi-clan wars, especially on maps like Layers because of the ease of capturing flags.
On maps like TDM maps like citadel and KotH maps like King of the Hill, multiple teams would work because the teams are all interacting. On CTF maps that is generally not the case, as the majority of the time it's just recons running at one flag over and over again. TDM and KotH would at least give the feeling of there being multiple teams at play.
Scoring would also be in question, as given that there are 4 different teams there should be 4 different score rewards handed out. My suggestion would be:
3 Points for the winner
1 Point for the runner-up
-1 Point for third place
-2 Points for last place
This could lead to scenarios where better clans could just farm worse clans more efficiently, but that happens anyway so who cares. I think the point is that multi-clan wars need to be carefully implemented otherwise it could lead to a lot of problems
Great idea; each map needs to be optimized for a well-thought-out appropriate amount of teams. E.g: A map like citadel would need 4 teams to be kept fair. If there were only 3 teams. there would be significantly more teamwork against the red team by the blue and green teams.