It is possible to be in more than 1 rich media engagement at a time.
Whenever you are engaged with a visitor and you switch to another engagement tab the other visitor(s) will be placed on hold. For the visitor, this will be signified with a pause button over your photo (if engaged in chat) or audio/video feed (if in a rich media engagement).
Chat visitor on hold
Audio/video visitor on hold
The on hold alert timer will alert the operator to visitors who have been on hold for a given period of time to help minimize wait times.