Final answer:
Duke Orsino asks the musicians to continue playing music to indulge his overdramatic love for Olivia, hoping to cure himself by overindulgence.
Step-by-step explanation:
Duke Orsino in Shakespeare's Twelfth Night asks the musicians to play on because he uses the music as a way to fuel his obsessive love for Olivia. The music for him is like food for love, and he desires to have an excess of it in an attempt to cure himself of his unrequited love. He hopes that by overindulging, his appetite for love may grow sick and die out. This metaphor illustrates his melodramatic and indulgent nature, a common characteristic of characters during the Renaissance period.