Legal Question in Administrative Law in California

There are some serious problems with the concept. First, a power of attorney is a rather formal arrangement between a principal and an attorney-in-fact which carries with it a requirement that the principal be competent at the time the POA is granted. A person with Alzheimer's may or may not be legally competent to execute or modify a POA.

Further, the Probate Code, which governs powers of attorney in California, provides that when two or more persons hold POAs for the same principal, the authority granted may be exercised only by unanimous action. This is true whether a single instrument names both, or whether the two attorneys-in-fact are appointed in separate instruments.

Therefore, rather than trying to execute a new POA or to modify the existing POA to include both names, I'd suggest that you consult with a local attorney who specializes in "elder law" or conservatorships, and inquire whether, considering your mother's current competency and overall family needs and objectives, a replacement POA is possible or whether your mother should be placed in a conservatorship or guardianship.

In any case, I doubt that both you and your sister holding powers of attorney is a solution.