There are rumors that Colin Firth (“The King’s Speech,” “Pride and Prejudice,” “Bridget Jones’ Diary”) may be the new Professor Henry Higgins in a forthcoming remake of “My Fair Lady,” to be directed by Joe Wright (who directed the Kiera Knightly version of “Pride and Prejudice”). Carey Mulligan of “An Education” might play Eliza Doolittle.

I am skeptical of remakes in many circumstances, and of course the George Cukor version of My Fair Lady with Audrey Hepburn and the divine Cecil Beaton designs is unquestionably iconic. I side with Cary Grant, who, asked to play Henry Higgins, famously said that not only would he not accept the part, but unless Rex Harrison repeated his Broadway performance on screen, he wouldn’t even go to see it.

In my dreams, though, I try to imagine a version with Grant opposite Harrison’s Broadway co-star, Julie Andrews. It would have been great. And so, just as the plays of Shakespeare are constantly new again for each generation, so can other stories. We saw a terrific production of “A Comedy of Errors” last week, in a sort of fantasy Edwardian setting, with a opening act introducing us to a small modern-day British acting troupe who would be performing the play, so that the real life actors were playing contemporary actors playing an early 19th century version of a 16th century Shakespeare about confused identities. And don’t forget, Shakespeare was doing his own version of a play dating back to ancient Rome.

And of course “My Fair Lady” itself is the musical version of “Pygmalion” by George Bernard Shaw, inspired by an ancient Greek myth. “Pygmalion” was made into a wonderful film under Shaw’s personal supervision, with his choice to play Eliza, Wendy Hiller, and Leslie Howard as Higgins. I have always been fascinated by Shaw’s decision to chance the ending of his play for the movie version. In the afterward he wrote for the play, Shaw makes it very clear that Eliza and Higgins have no romantic future; he explicitly says that she marries the hapless but doting Freddie. After all, the story not a romance; it is about class and politics and religion and ideas — like all of Shaw’s work. But when it came time to write the screenplay for “Pygmalion,” he could not help reverting to the myth that inspired its title and at least leaves the door open for the idea that Eliza and Higgins fall in love, and that was carried over into “My Fair Lady.”

It is exactly one century since Shaw’s “Pygmalion” was written, and 55 years since “My Fair Lady” opened on Broadway. Shaw could never have imagined that class barriers would dissolve as much as they have. And yet, the play has enduring relevance and appeal. I think we’re due for another try, don’t you?