An update of the setting of a play by Shakespeare to modern times could be found in an adaptation. Adaptations often take a book, film, stage play or television series and change it while maintaining its essence. For example, the 1999 movie <em>Ten Things I Hate About You</em> is an adaptation of <em>The Taming of the Shrew</em>, by William Shakespeare, set in a high school with teenagers as protagonists.
The style is called "Call and Response" : )