I have a General Durable Power of Attorney for a family member. covering property, finances, medical et al. Another person has a Durable Medical Power of Attorney for the same family member.
Generally, the one signed most recently controls in the event of a conflict. Most "general" powers of attorney are financial, not for making medical decisions, so there is usually not an overlap: one controls finances, the other controls medical decisions. An attorney should carefully review the wording of both powers of attorney to adequately advise you.