I am thinking of implementing multiple ending to one of my novels and it would be done the following way: There's a scene where the main character is about to do something, but I leave it to the reader's imagination and then wrote 3 different last chapters to let the reader choose the ending that they deem the best. What are some other ways you think multiple endings can be implemented in a novel, preferably backed by a famous author, and what are the pros and cons?
By offering multiple endings to your story, you are distancing the reader from the story, and breaking their immersion. In effect, you are saying, very loudly, as the narrator: "it could be that X happened, or Y, or Z, but I won't tell you which." So, you're moving the focus from the story to the narrator. You're implying that "what actually happened" is of lesser importance than some other factor.
The Princess Bride does in fact suggest multiple endings to Buttercup's story:
'And they lived happily ever after,' my father said.
'Wow,' I said.
He looked at me. 'You're not pleased?'
'No, no, it's just, it came so quick, the ending, it surprised me. I thought there's be a little more, is all. I mean, was the pirate ship waiting or was that just a rumor like it said?'
'Complain to Mr. Morgenstern. "And they lived happily ever after" is how it ends.'
The truth was, my father was fibbing. I spent my whole life thinking it ended taht way, up until I did this abridgement. Then I glanced at the last page. This is how Morgenstern ends it.
Buttercup looked at him. "Oh my Westley, so do I."
From behind them suddenly, closer than they had imagined, they could hear the roar of Humperdinck: "Stop them! Cut them off!" They were, admittedly, startled, but there was no reason for worry: they were on the fastest horses in the kingdom, and the lead was already theirs.
However, this was before Inigo's wound reopened, and Westley relapsed again, and Fezzik took the wrong turn, and Buttercup's horse threw a show. And the hight behind them was filled with the crescendoing sound of pursuit...
However, The Princess Bride is notable for being very meta with its story, throughout. The narrator's voice is not only very present throughout the text, but he actively discusses the way the story could be told differently by different "narrators". The whole story is seen through a meta prism, as it where.
Ways I've seen:
The choose your own adventure option, where you give them a list of possibilities and tell them where they are.
The Lord of The Rings option where you just sequence the endings and end the story over and over again.
The Princess Bride option Galastel mentioned.
The multiple epilogue option. This is basically like your multiple chapters, except they're called epilogues so the reader knows the story is basically over. They could each have a descriptive title so the reader understands they're options.
You could direct the reader to a web page where you have different ending options on a menu. This option may be more technically difficult, but it's not hard, and you could then get some metrics of how popular each of the endings are, and even graph it over time. I mean, that doesn't show which ones people necessarily thought were written the best, but you get to see which ones people look at the most. It would probably also encourage online reviews and commentary that you really probably shouldn't search for because some people can be really abrasive. (I have seen this done, I just don't remember what books. I think one of them even had an option on the web page where they let people write their own, with a checkbox to say whether the submitted versions could be shared, and they then reviewed those submissions and released a few of them. But it was a long time ago and I don't remember what the book was.)