I'm going to start this blog by proposing that you as a writer are faced with one of the three opportunities:
A - A film company is remaking movie X and wants you to write the script
B - A publisher wants you to write a new addition to popular fiction series Y
C - Famous author Z left an uncompleted work and their publisher wants you to finish it.
Each of these offers of course with the requisite promises of fame and fortune, so the question is would you take any of these offers?
So here's my take. As far as A goes the response has to be, 'which movie?' If someone is planning to remake Casablanca or Citizen Kane then it has to be a big fat no. The simple truth is that the best you can hope for with a classic is that the critics and film buffs won't call for your summary execution. On the other hand there are plenty of movies that had the potential for greatness and fell flat, that might be a challenge worth taking.
B is another 'maybe' scenario. There are series that have enough 'white space' in them that a new story could fit in easily, consider James Bond or Sherlock Holmes, new stories have been created around those characters for years and some of them are pretty good. On the other hand there are series with a tight narrative structure where a new story would be downright ridiculous, who in their right mind would take on creating a fourth chapter of 'The Lord of the Rings' for example?
C is by far the easiest to answer, basically no, nyet, non. This option is a poison chalice. The fundamental problem is that whatever you do, however brilliant you plot and dialogue and it is never going to match up with what the fans of the author imagined, you are doomed to disappoint whatever you do.
So would your answers be the same or would you bravely throw yourself into the fray?