Hi. I'm currently figuring out how to implement a recent messages user interface (MDL-25616). Conceptually similar to your email inbox but for all of your Moodle messages and notifications. A single place that will show you all of your messages in chronological order.
Below are three possibilites. Suggestions for other alternatives are welcome
1) Show all conversations in the same 2 pane layout as is used for 1 on 1 conversations. Shows everything in a single flow which is nice but could be rather cluttered. The interleving of conversations could also be a bit confusing.