This kind of story relies on what TV Tropes calls ‘The Alternate Self’.
I doubt Sliding Doors (1998) was the first well-known story to use this structure, though it is perhaps one of the best known, since more people watch popular movies than read books. This is a plotline in which a character has a difficult decision to make. Instead of having the character choose one path, then carry on the story until a good point to stop, this kind of story decides to explore the consequences of each decision by having the character follow both paths, perhaps with alternating chapters or something quite complicated plotwise.
This kind of plot can be quite didactic. Usually this sort of story has the following message:
However you imagine your life might have been had you made X decision instead of Y, your imagined other life isn’t as romantic/glamorous as the imagined life in your imagination.
Here are some examples of books which use this plotline.
THE POST-BIRTHDAY WORLD BY LIONEL SHRIVER (AMERICAN AUTHOR, SET IN ENGLAND, DARK)
Anyone who has read Shriver’s later (and better known) We Need To Talk About Kevin will already be expecting something quite dark. It’s what Shriver is good at. I thoroughly enjoyed this story. Shriver is an expert at plotting, as evidenced by her adept execution of this device, which is used for the end purpose of exploring long-term, stable relationships such as in marriage. The end message, for me, was that
…the story breaks into two narratives with alternating chapters: In one, Irena pursues an affair with Ramsey and leaves Lawrence; in the other, she restrains herself and stays loyal. Each choice has its downside.
I think that this book is just as good as We Need To Talk About Kevin. Don’t be fooled by the cover; the bright colours may suggest chick-lit, but it is nothing of the sort.
JUST LIKE FATE (Young Adult)
I have not read this one myself, but here’s what Kirkus had to say:
In an ambitious narrative device, the book juggles two alternating plots, following a prefatory “Before” section. Chapters titled “Stay” are based on the premise that Caroline chooses to remain with her grandmother in the hospital and hears her dying words of love for her granddaughter; in those titled “Go,” Caroline succumbs to her friends’ pressure to go to a party, thus missing the moment when Gram dies.
ME MYSELF I BY PIP KARMEL (AUSTRALIAN CHICK-LIT)
This is a book from 2000 which has been adapted into a film starring Rachel Griffiths. This is much more light-hearted than Shriver’s, and makes use of a structure oft-utilised by writers of picturebooks. When the protagonist comes back from the fantasy world (or in this case, wakes from a vivid dream), they are lead to believe it wasn’t really a dream because they have brought something back with them from the ‘dream world’. Or things have been moved slightly, and their world view is significantly changed (in almost all cases, for the better).
LIFE AFTER LIFE BY KATE ATKINSON
Atkinson’s (Started Early, Took My Dog, 2011, etc.) latest opens with that conceit, a hoary what-if of college dorm discussions and, for that matter, of other published yarns (including one, mutatis mutandis, by no less an eminence than George Steiner). But Atkinson isn’t being lazy, not in the least: Her protagonist’s encounter with der Führer is just one of several possible futures. Call it a more learned version of Groundhog Day, but that character can die at birth, or she can flourish and blossom; she can be wealthy, or she can be a fugitive; she can be the victim of rape, or she can choose her sexual destiny. All these possibilities arise, and all take the story in different directions, as if to say: We scarcely know ourselves, so what do we know of the lives of those who came before us, including our own parents and—in this instance—our unconventional grandmother? And all these possibilities sometimes entwine, near to the point of confusion.
– from Kirkus