Creating and rigging a full character turnaround can be achieved by creating multiple deformation chains on a same character without having to create completely different puppets.
For a simplified process, you can keep each view of your character separate in the Timeline or Node view. If you create separate rigs for each view, then you can simply turn on or off the exposure of each view in the timeline when needed.
However, if you want to keep the entire character, with all views, in one group/rig on the timeline, then you can follow the process described here by building a multi-pose deformation rig, also known as multiple transformation chains.