Well thanks for the suggestion, by the way the main reason is that nobody asked this before. All our customers are used to show both private/public chat stacked together. by the way to increase the component flexibility i think that it will be a good feature to add.

Maybe a quick solution would be use the chat rendering as a module, then use CSS to move the private chat box to the right hand corner. Applying a fixed positionment to the private chat you will have a mixed mode.