Sure. There are two ways to use that original piece. One, as a reprint. (I just blogged about selling reprints [second rights] of your article to another editor, or to many other editors. There is no exclusivity for reprints.)
The second way is to simply take the research from the first article, move the words around, query about the new piece, and sell it again.
Let’s focus on the second approach here. You can use the contents of the first article to create a different one, or many different articles. Each is the original article rewritten. Each must have its own identity, and each rewrite (since it is a new, different article) can be sold like any other article: all rights, first rights, simultaneous submissions, and so on. Even later as a reprint!
A rewrite will likely use some or all of the research material used for the original. (It almost always uses more, different information, quotes, or anecdotes too.) What’s mandatory is that the resulting article be unique. The best way to refocus a rewrite is to find a different angle or slant to the theme, put it in a different place or culture, or emphasize the history of the first article.
You first article might talk about the Chicago Cubs since 1876, when the National League began and the Cubs won the first pennant. A rewrite might talk about 1876 only, the Cubs, and that specific pennant. A different rewrite might focus on Anson, Spaulding, and the luminaries of that year; another might discuss the greatest Cubs from 1876 to the present.
When are rewrites most commonly done? When you have sold first rights to an article and you want to spin off more sales from the piece and its research. Even if an editor has bought all rights to the first item, he has only bought the copy, not the idea. You can reuse the idea and much of the original copy in different ways.
The key question is, how much must subsequent rewrites differ from the original, and other rewrites, to have its (or their) own legal identity. That’s hard to answer. Surely if you change the title, lead, conclusion, and quotes, that ought to be difference enough. Another approach is easier, though: change the angle. Come at the topic from a different tack. That will require a new title. The old lead won’t work, and since the conclusion is intimately linked to the lead, it too must change. You could even use some of the old quotes, since they refer to a different base.
The selling process is identical to selling an original article. But must you reveal that you have a similar article in print? It’s your choice. You don’t have to. But as long as both are clearly distinct, doing so might enhance the rewrite sale.
(There’s a lot more about the writing, selling, and reselling process in my Travel Writer’s Guide.)