A method is provided in one example embodiment and includes receiving data associated with a plurality of endpoints that are engaged in a video conference, and evaluating whether a first endpoint and a second endpoint of the plurality have entered into a conversation such that a conversation mode is triggered. Once the conversation mode is entered, the first and second endpoints of the conversation are rendered on two different screens of a video display. In more specific embodiments, the method includes analyzing active speaker patterns of some of the endpoints to determine whether to enter into the conversation mode. In still other embodiments, the method includes determining whether the rendering on the two different screens is temporary or made permanent for a duration of the video conference.