It is a sight for the onlookers when more than one person speaks at a time or when a team engages in endless discussions. Outsiders (non-team members) would start labeling such teams with tags like "indisciplined", "very political", etc. Sure enough, it is not the subjected team's desire to end up in such a state and even worse that such state becomes more or less a routine thing during stand-up.
In my experience and observation, it takes a lot of courage, discipline and mentoring to have one conversation at a time in a meeting. In order to restore this discipline of "one conversation at a time", play the license to speak game. Yes, you read it right, I called it GAME. It is more a fun to gamify the thing called DISCIPLINE.
So what is this game all about? Well, this game is all about the eligibility of a person to speak in a meeting. One who holds the 'declared token', has the license to speak and after his/her turn, the token is passed to the next person in the team, who then gets the license to speak/update.