Our area tried one principal for two schools because of cell phone coverage and cost reduction. Principal would spend half a day at one school and the second half at the other.
It worked too well. So, when the economy turned around, they went back to two principals.
A friend, a real teacher and a superb principal worked for 8 years after he retired as either a half time principal or a full one for two schools during the Obama economic down. turn.
He said that with cell phone coverage and good police support, he could have handled 3-4 schools. If a kid really misbehaved, he would have the cops go to the school, get the kid and put him/her in the back of a squad car and take them to the local police headquarters and detain them until he arrived and the parents. Usually that was only needed once. He told the parent if the kids did not behave, they had to home school them.
That should be a very effective strategy. A bit extreme and involved compared to a paddling and parent conference but if that is the only tool left use it.
It is a shame that the principal has to be a disciplinarian at all.