Having excluded a fixed time explanation for The Jacket, we turn to the possibility that it might be resolved by multiple dimension theory. This solves the problem of changing the future, because Jack could visit the future in which Jean dies, then travel back to another universe (whether he creates it or moves to it) in which he alters events so that Jean lives, without changing the future history of the world in which she dies.
Here, though, we have the problem of getting that far in the story, and it lies in the predestination paradox which the fixed time approach resolved so neatly last time. When Jack is in the future he learns that something he told Doctor Lorenson enabled her to cure Babak, and he discovers what that was; when he returns to the past, he tells her what she told him. However, he must have begun in a universe in which he never told her, and thus it is very difficult to see how he could have come into a universe in which he had already told her--every iteration of Jack leaves with no knowledge of Babak, and even what Jackie reads about Babak is itself dependent on Jack telling Doctor Lorenson how to cure him. Thus no version of Jack can enter a world in which he has already told Doctor Lorenson how to cure Babak without coming from a world in which he has already done so. That universe cannot exist, and cannot come into existence.
To clarify, for Jack to bring back word of how to cure Babak, he must land in a future in which he has already done so; but such a future can only exist if there is a version of Jack who already landed in such a universe, and such a universe can only exist if there is a version of Jack who has already landed in it. What is simple for fixed time theory proves to be at best convoluted and more likely impossible for multiple dimension theory. Jack cannot arrive in the future of a universe which he cannot have caused to exist.
Nor is this resolved by Jackie's discovery of the Babak case in her research. She found it because it was connected to events following Jack's death; it was so connected because it happened at about the same time, because Jack gave Doctor Lorenson the needed clue. Without Jack's help, it is unlikely in the extreme that Babak would have been cured at that time, if ever; equally unlikely is that Doctor Lorenson would have mentioned or discussed Babak without the connection between him and Jack.
There thus seems to be no way to get the history in which Jack obtains information about curing Babak from Doctor Lorenson in order to give it to Doctor Lorenson, and our multiple dimension theory solution fails.