You need to open yourself to a variety of roles. Of course, there is still the question of auditioning and actually securing the role that you're looking at.
"Noel [Coward] and I were in Paris once. Adjoining rooms, of course. One night, I felt mischievous, so I knocked on Noel's door, and he asked, 'Who is it?' I lowered my voice and said 'Hotel detective. Have you got a gentleman in your room?' He answered, 'Just a minute, I'll ask him.'" (Beatrice Lillie)