@equipe v11​ ! We have a beta (at the moment there are a few limitation on number of people who can be opted in for the beta) which allows you to prevent visitors/users opening more that one conversation at a time. Here is a screenshot to show how you can control it in the Messenger settings. This will work only for web users. If you are interested please open a conversation from the Messenger in your workspace so teammate from support will be able to guide you further on this.