One of the easiest ways to change the dynamics of a meeting is to simply change the body language.
You can’t change a person’s mind until you change their body language.
Test it out and see how the body language immediately changes when people agree or disagree with what is being said.
So if the meeting is going south, stop and say, “Let’s take a quick five-minute break and come back.” Or get coffee for everyone in the room. You can also try handing out information so people have to physically change their body language.
You can also simply stop the meeting and redirect it. Say something like, “Let’s step back for just a minute. I want to make sure I have correctly grasped what is important to you and what we want to accomplish today.“ Then repeat the goal of the meeting, allow them time to expand on anything, and verify that you understand what they said.