My mother's power of attorney lists 3 agents, including myself: X and X and X. Does this suggest that we must act together or can one of us act independent of the other two?
There is no other wording regarding whether we must act in concert or can act independently.
This seems to require unified action. I would often draft a power of attorney with multiple agents to specifically say that only a majority or that any one could act. I think that you will find most banks and other entities reluctant to act without all signatures. There may be a way to delegate powers or one or more of you could refuse to act. However, if the remaining agent can no longer act this might require a guardianship
Based on the information provided, I would agree that the POA document requires all three of the Agents to act together. Depending on the language set oout in the document, one or more of the named Agents might be able to relinquish their authority to the other named Agent(s).