Hello tjbrunetto, and sure you can!
There are two main approaches to this: the first consists in just creating the alternative frames of the whole character, and activating them while deactivating all the other attachments for just the couple of frames you need to make it turn.
This has the advantage to be quick to rig, but it doesn't allow much freedom.

A second approach, longer to rig but with a great deal of reusability, is to add the alternative angles for each image of the skeleton, and create a turnaround animation.
You'd then be able to copy the frames from the turnaround animation and orient each piece as you see fit, being able to turn just the head, or any part of the body, while also being able to keep the framerate of your overall animation.

You can see two examples of such rigs here:

And you can download these projects as well as see the complete rigging process at this page:
Spine: Twitch

No problem! Should you have any doubts about any part of it I’d be happy to help you