Yeah, it would bring another dimension to conversations if the whole party could take part.
I remember from playing through DOS2 in multiplayer that the element that actually caused the most friction and was most disruptive to our suspension of disbelief was always having to negotiate and argue over who of us should do the next conversation.
Something like this would ensure that everyone is engaged and included in the story.
For inspiration you could take a look at how Bioware handled this exact feature in Star Wars: The Old Republic.
In that game, all players see the same dialogue options and can chose any of them. After everyone has chosen an option, the game rolls a dice for each player, and whoever rolls higher is the option that will be picked and the player that will speak.
