Theoretical Groundhog Day (movie) question. Could there be more than one person suffering like Bill Murray did?

Bill Murray’s character was caught in a repeating cycle that didn’t let him escape the repetition until he turned into a decent guy.

Is it possible that the same cycle could have applied to other people – women, for example? Could he have met a woman on one of his days, fallen in love that day, and kept repeating with her?

Does the movie ever say any thing about this being a one-off? Or is the implication that anyone can experience it?

Could people synchronize?