Could a writer redo & make a novel based on a well known story?

Question:

Could a writer redo & make a novel based on a well known story?

Take disney stories like snow white & cinderella or the lion king & little mermaid.

Best Answer - Chosen by Asker: some writer have done similiar things to that, such as Wide Sargasso Sea by Jean Rhys , and Rosencrantz and Guildenstern are Dead by Tom Stoppard (i think) where in both cases minor characters in Jane Eyre and Hamlet respectively were given a created story with them as main charcters, while the main characters in the original storys were backgroung or just a small mention.

there have also been some film stories created on well known books, such as Clueless being a modernised version of Austen's Emma, Bridget Jones Diary being loosely based on Pride and Predjudice