Maybe. It all depends.
You write a question that describes scene #1, then flag it as a dupe of an existing question. You write another question that describes scene #2, and flag it as a dupe. Repeat for every scene in the entire story.
Don't do that. It should be fairly obvious, but this is a straightforward abuse of the system. Having lots of different questions about the same story is simply not very useful, and it may distract people who are looking for other stories that happen to have similar events.
You see an already-answered question which is really vague. It describes the story in the simplest terms and barely gives enough information to go on. There are a good half-dozen answers, all pointing to different stories, and all upvoted to some degree.
This is surprisingly common. Quite a lot of story ID questions, especially older questions, are just not specific enough to uniquely identify a single story. Unfortunately, you can't edit the question to make it more specific, because that would invalidate upvoted answers (which is generally frowned upon). So asking a separate dupe may be the only way of getting this information into the system. In that case, I'm not sure it should be characterized as abusive per se, but you should definitely make sure that your question is very well-written and detailed. It's probably also a good idea to provide a high-quality canonical answer at the same time, especially if the original question's answers are basically just a bunch of "Is it [Title]? How about [Other Title]?" one-liners. Then you can dupe the old question against the new question instead, because the new question will be superior.
Still, deliberately asking dupes is not something you should be making a habit of doing. The system doesn't like it when you have a lot of closed questions, and (in general) you can get question banned for it (but I'm not 100% sure if that applies to duplicates in particular). Regardless of particulars, asking and answering new questions is on the whole a more helpful and productive activity, and will likely earn you more rep in the long run.
Another consideration is how many other people are asking about it. To borrow the words of Isaac Asimov:
Then, too, it has had the strangest effect on my readers. Frequently someone writes to ask me if I can give them the name of a story, which they think I may have written, and tell them where to find it. They don't remember the title but when they describe the story it is invariably 'The Last Question'. This has reached the point where I recently received a long-distance phone call from a desperate man who began, "Dr. Asimov, there's a story I think you wrote, whose title I can't remember—" at which point I interrupted to tell him it was 'The Last Question' and when I described the plot it proved to be indeed the story he was after. I left him convinced I could read minds at a distance of a thousand miles.
For some reason, some stories are just more memorable than others. They stick in our heads, and turn into Story ID questions. If a story is highly memorable, it's likely that other people will have written other Story ID questions about it. You should go looking for those questions, and if they already have the relevant details, then obviously you should not post another dupe with the same information (but you may be able to post a high-quality answer, if the question doesn't yet have one).