It sort of "lessens" the ending for the first story though. I mean it's one way to get around the issue, but the endings in the previous story would have to be fairly similar in the first place. If you became a demon king in one ending and a master paladin in another, you're going to have a time of it trying to come up with a logical beginning to the second story to explain how those endings could wind up as the same beginning for the second story. Youd probably still sort of need to choose a few of those endings as canon.
I suppose making a lot of time pass (Like decades) that it makes the events and outcome of the last story "hazy" could work, like nobody really directly addresses what happened or only hints of what might've occurred. But you still have to have similar endings for it to work so you're probably still choosing a few of those endings as canon.
The only way you could really do it, is if the next story in the series offers choices at the very beginning that link up with the various winning endings from the first story. That's sort of cumbersome though.