Answer:
The powers available to the POA should be spelled out in the POA document and also vary by state law. If you're not sure whether or not the attorney-in-fact has the authority to add or change beneficiaries, ask bank counsel to review the document prior to permitting any changes.
Many states provide for statutory which generally prohibit the POA from changing ownership on any assets or otherwise gifting the assets to others. Again, this will vary by state law.