During the course of interaction with my clients' companies, a lead can be handed over to several different people (from prequal to sales to setup to support). Likewise, the different communications in conversation may need to change hands as well. It would be nice if we could assign a conversation to a rep, and upon completion (maybe a button to mark it as resolved or complete) remove them so it goes back to their main representative (the one assigned to the lead). Kind of like having an observer but also being able to see that right now the communication is "owned" by a specific user.
Additionally, since sometimes those communication need actions from multiple people, being able to add tasks and assign to those users from within the communication would be helpful, so you don't have to switch tabs or go back and forth between different screens.