Can a medical power of attorney add an alternate to share responsibilities?

No, the only person that can add an alternate is the original person that granted Power of Attorney. This is a duty that cannot be delegated without the express permission of the one who granted POA.

Understand that medical POA is not an obligation to hands on care but the authority to make medical decisions should the grantor be unable to express their wishes. There are many tasks that you can share without the need to have a legal document: arranging and assisting with transport to medical appointments and homecare, fact finding, even sitting in on appointments and getting test results if the person is given HIPAA permission by the patient.