I think Google Wave (now Apache Wave) did a good job on delivering a better multiperson email experience, but I think it fell short as a replacement for instant messaging. In particular, the keyboard shortcuts are awkward for that use case.
I have a few people that I instant message regularly and prolifically. To one poor soul I write a novel's worth of messages every year. There are a few features that would make communication better in this situation.
The first is that I wish that there were a way to fork the conversation, so that I could have two conversations with the same person at the same time. Often I have multiple things to talk about, or discussion on one topic will spawn conversation about another topic. (I'm very scatterbrained.) That topic could again be subdivided, indefinitely, as necessary.
The fork point in the main conversation would have an indicator pointing to the new conversation. You could then switch back and forth between the topics, reading and writing as things come to mind. A "news feed" of intermingled messages would probably be the easiest way to read it in real time, but when looking at history everything should be separated into its proper conversation.
Where this arrangement really shines is when revisiting old topics. Right now, I have to prefix my statement with "remember a few months ago when I was telling you about X?". Now, instead, I can just find the old conversation and add more messages to that topic.
Another important feature would be that it wouldn't necessarily need to notify the other party of the messages aggressively, such as by using phone push notifications. Instead the other person can participate actively or just check once a day.
Perhaps this sounds like it could be done over email, but I've found that email requires me to organize my thoughts too much. Even picking a subject line is difficult and detracts from getting my thoughts out on paper.
While I would like to have this user interface for one-on-one conversations, it would probably work even better for small groups. Also, I believe I'd also use it to "chat" with myself, organizing my thoughts.
Email comments or corrections to chatterbox at this domain.