Learn to be calm while on the air. Often operators get worked up a little when they are on the air, like stage-fright or trying to do the right thing. If operators remain calm more often, more actual real communications go on.
For all of the great examples listed already, keeping the conversation calm will help loads. There is no need to jump on before the other operator jumps off. The break in transmissions should become a natural habit of your operating practice.
Once you have an emergency situation which requires someone to be the command operator, usually that responsibility befalls the trail leader. This should be classified as a "net coordinator". This person says who talks and when. When the emergency is over, normal operations resume.
On the GTR when Team Nakman was hanging precariously from the ledge, too much confusion arose. Instead, the emergency call should have been put out, and the trail leader (Me) should have announced to keep the frequency open only for emergency traffic. It would have gone better. As it was, fragments of info were getting passed around like rumors in high school, and I had no idea there was a problem until 15-20 later.