Is it possible in Character Animator to have Front, side, and back Puppets

The walk behavior supports several profiles for walking and standing. There is also the Head Turner behavior that supports profiles based on which way you turn your head. There are not 6 profiles, but its the same idea. You can put triggers on the profiles instead of using those behaviors then put the triggers in a swap set. Then you can have 6 profiles in the one puppet, with a trigger to pick the profile to display.

But it will just jump the artwork displayed - if you are trying to move the camera around, it is your responsibility to update any background or other things in the scene.