Some thoughts and definitions:
Let's take a book we all know--Frankenstein.
Let's write a sequel: maybe the monster survives and gets involved in someone else's family; or returns to finish off the Frankenstein family; or Victor leaves the experiment notes to Walton, who, his hopes blasted by a failed arctic expedition, decides to become a pioneering biologist. We all know what sequels are.
Of course, we could write a less direct sequel--take a hundred years or more off and see where the story is then. (In a way, Young Frankenstein takes this route.)
But why would we write a sequel? Is there some part of the story that needs concluding? Is there some theme that we want to explore?
Eh, sequels are boring--let's write a re-imagining: we'll pretend that the Frankenstein story didn't take place and we'll move the basics of the story to another time or setting. During World War I, a crazed surgeon decides to solve the problem of war with a super-soldier. During the 1990s, a hacker creates an AI that gets out of control. Etc.
Or let's play with re-imagining the story for a different genre: mix Frankenstein with Cinderella for a fairy tale of making a true love; mix in some slapstick comedy for Young Frankenstein; mix in some Western material and you have a monster running amok or destroying the railroad or fighting off US cavalry. Etc.
(Of course Frankenstein's monster would fight for the Native Americans--he's obsessed with them in the original.)
But do we really need another re-imagining? Let's write a parallel novel: let's re-tell the original story from a different POV. Some examples: John Gardner rewrites Beowulf as Grendel; Gregory Maguire rewrites Oz as Wicked; Alice Randall rewrites Gone with the Wind as The Wind Done Gone.
So let's tell the Frankenstein story from Elizabeth's POV--how'd she feel when her beloved brother/husband goes off to play with dead things? Or what about William or Ernest, the little Frankenstein brothers? Or Clerval, Frankenstein's put-upon friend? Or maybe Robert Walton's crew has something to say about this crazy dude they picked up off the ice?
But do we really need that?