Two of the biggest female movie stars of the 1950s were Monroe and Holliday.  According to Jeffrey Lyon’s Stories My Father Told Me: Notes From “The Lyon Den,” the great Judy Holliday did a smashing Marilyn Monroe impression on a TV show in early 1955—remember shows were filmed live in New York at that time.   Like most of these old anecdotes, this one may be apocryphal, but if we’re to believe Lyon’s father, Leonard, who wrote the Lyon’s Den syndicated column for 50 years from which his son’s book is compiled:

…the next day, monroe was walking with a friend down Fifth Avenue and passed Holliday.  “I hear you do an impression of me,” said Monroe.  “I’d love to see it.” They made a date, and the next day, over tea, Holliday showed it to her.

A few days later, Holliday had an important appointment and dressed carefully for it.  “You look like a real woman,” said a friend.  “I thought I was a real woman,” she replied, “until Marilyn Monroe came over to my house for tea.”