You can do whatever you like AP as long as there are no duplicate copies on Medium at the same time. Publications may or may not accept it. One of my boosted stories was republished in the same publication this year as last year. The only thing I changed was the links to recommended reads at the end.

You can just edit an old story but that won't give it a new date and may not improve circulation.

You can also write a different version of the same thing and the two can be on here together as long as they are substantially different.