What screenplays were rewritten, in order to be a sequel to an existing franchise?

When I was first breaking into screenwriting and working mostly for Dimension Films, there was enormous buzz around a spec script called Deader written by Neal Marshal Stevens.  As the story goes, Bob Weinstein himself, went to the writer's grungy NYC apartment and presented him with a check for half a million dollars, purchasing it right then and there.  Everyone working on genre films at the time - executives, writers, producers, agents - read the script and agreed that while certain parts of it didn't quite make sense, it was one of the the scariest scripts we had ever read. However, the script got stuck in "development" at Dimension for a long time.  For whatever reason the project could never get off the ground. Years and years went by.  Finally, Bob impulsively decided to adapt the script for the established Hellraiser franchise.  My friend and fellow genre hack, Tim Day, was hired to do the adaptation, and instead of a higher budget, theatrically released film, it became the straight-to-video Hellraiser: Deader (http://www.imdb.com/title/tt0337636/fullcredits#cast) Unsurprisingly, through no fault of any of the writers involved, this splicing of one story and mythology to another did not turn out well. Another example, my friend sold a very funny spec script called, The Passion of the Arc (The Passion of the Christ had just come out) about a modern day Noah.  This original script became the basis for the franchise sequel  Evan Almighty, though in a bizarre twist of WGA rules and arbitration, Josh did not get credit on the film.

Ocean's Twelve was originally a  spec screenplay by George Nolfi called Honor Among Thieves. The plot was about a group of thieves in Europe, which was more or less the same plot as Ocean's Twelve. It was originally slated to be directed by John Woo, but when that didn't happen, Nolfi and Steven Soderberg adapted it to the Ocean's series.

Dirty Dancing: Havana Nights started out, bizarrely, as screenplay by Peter Sagal (of 's Wait Wait... Don't Tell Me! fame) based on a true story: Havana Nights is based on an original screenplay written by playwright and NPR host Peter Sagal, based on the real life experience of producer JoAnn Jansen, who lived in Cuba as a 15 year old in 1958-59. Sagal wrote the screenplay which he titled Cuba mine, about a young American woman who witnessed the Cuban revolution and has a romance with a young Cuban revolutionary. The screenplay was to be a serious political romance story, documenting, telling, among other stories, how the Cuban revolution went from idealism to terror. It was commissioned in 1992 by Lawrence Bender, who was rising to fame with his production of Quentin Tarantino's Reservoir Dogs and Pulp Fiction. The screenplay was bought by a film studio who requested several rewrites before deciding not to produce the film. A decade later, Bender decided to make a Dirty Dancing sequel, and the film was very loosely adapted from Sagal's script. Not a single line from Sagal's original screenplay appears in the final film and Sagal says that the only remnants of the political themes that existed in his script is a scene where some people are executed. Source: http://en.wikipedia.org/wiki/Dirty_Dancing:_Havana_Nights

I'm a confessed sequel-holic.  These are the ones off of the top of my head, but I know there are more.  I'll update if my memory returns... Die Hard was at one time considered as a sequel to Commando, starring Arnold himself.  Then the script became a story about terrorists taking a building hostage as a super cop comes to rescue the day. Die Hard 2 was based on the novel 58 Minutes.   http://www.amazon.com/Minutes-Basis-Film-Die-Hard-ebook/dp/B00BHBFG0A/ref=sr_1_1?ie=UTF8&qid=1385535363&sr=8-1&keywords=58+MINUTES Die Hard 3 was based on a hot spec script called Simon Sez. The hot spec script Simon Sez, which later became the third Die Hard movie, was considered for Lethal Weapon 3.  It should be noted that Die Hard 1 and 2 and the Lethal Weapon franchise were produced by Joel Silver. Highlander II was an original sci-fi script and was rewritten to inject the Highlander mythos to it resulting in one of the worst sequels ever made. Saw II was originally a script called "The Desperate", which was often deemed too violent and, upon the debut of the original Saw, was termed as too "Saw-ish."  The producers got hold of the script and it was rewritten to fit the Saw mythos. The Tears of the Sun TITLE was actually the title for a script that was to be the fourth Die Hard movie, possibly co-staring Ben Affleck, Bruce Willis' co-star in Armageddon.  Willis wanted the title for the eventual Navy Seals movie he starred in and promised the studio that if he could have the title he'd help develop what became Live Free or Die Hard, the fourth film of the franchise. The upcoming Fifty Shades of Grey is an adaptation of the novel of the same name, which was first written as a fan fiction sequel novel for the Twilight books. Minority Report was originally developed as a sequel to Total Recall.  The producer and Total Recall director Paul Verhoeven optioned the Phillip K. Dick story and decided that the tone matched what they had done with TR.  The script was written, Arnold was attached, but then the production company Carolco went bankrupt.  And Minority Report was in development hell for years before finally landing into Spielberg's lap.  For the rest of that story... http://io9.com/5887350/we-almost-got-total-recall-2-in-the-1990s

Die Hard 2 was loosely adapted from the novel 58 MINUTES by Walter Wager. Because Fox was in a leadership flux, the studio wasn't yet certain it wanted to develop a sequel to Die Hard, which was still in theaters. Former studio president and Die Hard producer, Larry Gordon, figured that as soon as Fox hired a new production boss the first order of business would be to order up a part two. So to to get ahead of the process, Larry hired me to adapt the novel as a possible sequel, only with the names of Die Hard characters changed. The first draft was finished days after Joe Roth was named as the new studio honcho. When Roth inquired to Larry Gordon about a Die Hard sequel, the producer already had the script ready to go. In another strange twist on the theme, when Bruce Willis first dropped out of Die Hard 3, producer Andy Vajna refused to pay me until I revised my draft of part three into a stand alone script he could finance for Sylvester Stallone.

Saw II was originally The Desperate, but since it was criticized as too similar to Saw and the producers needed an idea for the sequel, the script for The Desperate was modified into the Saw franchise. However, the original characters and traps were kept. Source: http://en.wikipedia.org/wiki/Saw_II

Funny that Die Hard was brought up, because the original Die Hard was actually written as a sequel to the 1985 Arnold Schwarzenegger movie, Commando. A sequel was written by De Souza and Frank Darabont, based on the 1979 book Nothing Lasts Forever by Roderick Thorp (which is, itself, a sequel to his 1966 novel The Detective, made into a film of the same name in 1968 featuring Frank Sinatra and Lee Remick), but Schwarzenegger was not interested in making a sequel as his previous sequel (Conan the Destroyer) was less successful critically and did not do as well domestically at the box office. The script was reworked with a new central character, eventually played by Bruce Willis, and was retitled Die Hard. The fictitious country of Val Verde is later nodded to in the sequel to Die Hard. Source: http://en.wikipedia.org/wiki/Commando_(film)

Not quite an answer to the question, but I know the stand-alone novel On Stranger Tides written by Tim Powers was adapted into the third Pirates of the Caribbean movie.

This is slightly different than the other examples but, Pirates of the Caribbean: On Stranger Tides (http://en.wikipedia.org/wiki/Pirates_of_the_Caribbean:_On_Stranger_Tides) was adapted from the original 1987 novel On Stranger Tides by Tim Powers (http://en.wikipedia.org/wiki/On_Stranger_Tides), which obviously shares no connection to the other three Pirates of the Caribbean films.