How do you handle a family member with multiple personality disorder?

Dissociation? Multiple personality or dissociative identity d/o is rare, but does exist. Behavior changes in a family member may have many other causes too. If concerned about your family member, help him/her get to physician for a check up, and tell the person and doctor why you are worried. The doctor will help by evaluating & examining, & recommending further steps needed.
Correct diagnosis? This is a rare (and controversial) diagnosis. I am convinced it exists. My experience with this disorder (did) is that it is a life long disorder that can be managed but not cured. It is almost always associated with childhood trauma. Patience, understanding, therapy, and stress reduction are key. Full reintegration of alters is rare. Medications can help, but over-medication is a problem.