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While it seems that this is unintended, when using the iTaSC IK solver rather than the default Standard solver, the deltoid bone follows the arm IK.

From rest pose to approximately 85 degrees (almost horizontal) this works fairly well.

Above this point the deltoid bone begins to lag and stretch, so that the mesh of the shoulder is wrenched out of shape. Even if all bones are returned to rest position (approximately) the mesh does not return to its original shape.

Should I take this to mean that MHX does not support the iTaSC solver?

I haven't tried the iTaSc solver for years. I recall that I had some problems with it around 2010, and then I forgot about it. So I don't really know.

Another thing that may have caused the shoulder to behave strangely are rotation limits. Limit Rotation constraints may cause bones to jump suddenly. In the current rig, all Limit Rotation constraints are disabled, but rotation locks are still effective.