There's been several failed attempts to write a successful musical about Marilyn Monroe over the years and no one has yet succeeded.
You may recall there was even a TV series, SMASH, about creating a Broadway Marilyn musical called BOMBSHELL. In that fictional success story the show had a fantastic score by the song writing team behind HAIR SPRAY and CHARLIE AND THE CHOCOLATE FACTORY which we regularly heard in the programme; the cast album's readily available and it's a treat.