Curio has a very minor role in Twelfth Night, only appearing in 3 scenes and only speaking in 2 out of those 3 scenes. His role can be considered the role of a stock character. A stock character is a character type that appears repeatedly within certain genres. Shakespeare made use of many stock characters, including ill-tempered wives, bragging soldiers, "clowns, outlaws, clever servants, [and] female confidants" (Dr. Schwartz, "Shakespeare's Plays: Comedy"). He especially frequently makes use of a "jester, fool, or buffoon" (Schwartz). While Curio does not have as a great a role as a character like Nurse in Romeo and Juliet, who especially fits the description of a clever servant, he proves to be very intelligent, sensible, and even compassionate, showing us that he fits the description of a clever servant stock character.
Among Curio's very few lines, one thing is said with the purpose of distracting Duke Orsino from his alleged suffering. After Duke Orsino opens the play by moaning over his feelings for Olivia, Curio suggests that Orsino go out hunting as a means of distracting him, as we see in Curio's line, "Will you go hunt, my lord?" (I.i.16). He then suggests that Orsino go out and hunt a hart, meaning stag. Whether or not Curio is deliberately making a pun out of hart in the same way that Orsino does in the next lines is unclear. If Curio was intentionally making a pun, he may have been subtly telling Orsino to stop sitting their moping and go out and do something about his lovesickness, which would certainly portray Curio's cleverness. At any rate, Curio is certainly showing wisdom in wanting to distract Orsino from his absurd suffering.
Curio even shows compassion the next time he speaks in Act 2, Scene 4 by respectfully doing Orsino's bidding. In this scene, again feeling glum, Orsino asks for some music as music is the "food of love." Specifically, he asks for a song he heard sung last night. When Curio says the singer is not present in the room and Orsino asks who sang it, Curio readily answers that Feste sang it, "a fool that the Lady Olivia's father took much delight in," and quickly goes to find him in the house (II.iv.12-13). Curio's willingness to find Feste to entertain Orsino with another song to feed his woes of love shows us that, while Curio may not agree with his master's behavior, he can certainly feel compassionate enough and respectful enough to do Orsino's bidding, showing us that Curio certainly fills the role of a clever servant stock character.