The protagonist of the TV series Awake lives in two worlds: one in which his wife died in a car crash, and one in which their son died instead. As we see it, he spends a day in Hannah’s timeline and then a day in Rex’s, alternating.
But (in the four episodes I’ve seen so far) no one ever asks him where he goes on the other days. On the other hand, if he lives each calendar day twice in sequence, he ought to be able to use knowledge of events unrelated to his family to win the occasional bet, and I haven’t seen him do that.
So I choose to suppose that his awareness forks each morning, and rejoins when he sleeps, so that he always has two yesterdays, neither preceding the other.