This is my suggestion.
You could try to launch to external image editor for flipping Horizontal morph-based head/character body.
1.) Select your character to composer mode, then pick head.
2.) Click Launch to External Editor.
3.) Click Horizontal Flip.
4.) Ctrl + S to save the modification.

Thank you, but unfortunately this metodth not work with morph-based speaking head. And CTA3 not allow more than 1 morph-based head on character. Hope in new version developers fix this situation.

Is this now possible in Cartoon Animator 4? I just animated a character and in the process of him walking and reaching the other side of the screen, I wanted to flip his Morph-based head. I wish there was a way of doing this without breaking the animation.