I'm not exactly sure how this would work, whatsoever. This idea is a pretty ambitious one, but you would really have to work on fleshing it out, since I don't know how to do that in this case.
Basically, what if, after the original Sword Art Online game shuts down and the players wake up, (you should probably also have the Fairy Dance arc occur before this as well), Kirito goes on some sort of journey to discover how he was able to surpass the system of the game to kill Kayaba and end the game.
I am entirely unsure of how this would work in any capacity, as I stated earlier, and it's highly likely you would have to include crossover elements if you wanted to make your job at writing this any easier. Honestly though, I think I'd prefer it if, this time, there were no crossover elements, or at least if they were kept to a minimum. This would be a very demanding fanfiction to write, however, so I understand if you would rather just include crossover elements or just straight up make it a crossover between two or more series.
Here are some recommendations I have regarding how things could go, if you choose for them to go that way: Kayaba should have significance in the story, even after his death. Asuna should not be forgotten about for the sake of Kirito's journey.
You could perhaps make Kirito have some kind of family heritage that led to his victory, or have it be an intentional move on Kayaba's part for the system to malfunction and Kirito to win the fight. (You can come up with whatever reasoning you want for that.) There are tons of ways you could choose to develop this kind of story, and so I'd rather leave all possible avenues open for the sake of creativity. The rest will have to be fleshed out by you, if you decide to write this.