Some facial mouth shapes for Piero:
Neutral Pose:

Up Max 1:

Extreme Pose Down at Max 2:

Out Max 1:

In Max 1: Manual Corrections in "Edit Mode" since the Mesh without the "Subsurf Modifier" isn't dense enough for "Sculpting":

On the way to the creation of a "Corrective Shapekey" for Piero when his lower beak "drops down": "Join as Shapes" executed on the mesh duplicate:
