The casting and antics of secondary characters underscores the blatant sexual farce of the piece; they include Pan, a satyr, usually sung by a bass; Satirino, a baby satyr, sung by either a mezzo or a male alto; an elderly yet virginal nymph, Linfea, often sung by a tenor or countertenor, who is ravished by the satyrs late in the show; and the shepherd Endymion, who may be sung by a male singer or by a contralto!
And what about Calisto's virtue, amidst this tumultuous jumble of lust? Ever vigilant about her spouse's lecherous forays upon Earth, Jupiter's wife, Juno, calls upon the Furies to turn the princess into a bear, and Jupiter counters by using his powers to make Calisto a star, so to speak. (Presumably his sexual attraction stops short at fur, as he does not metamorphose into a bear to continue the chase....) On a clear night, look up, and pick out Ursa Minor. That's Calisto, folks.
Hisuteness of a non-ursine kind creates the dénouement in a 20th century opera by someone you might not expect to produce a cross-dressing role: Igor Stravinsky. In his one-act 1922 Mavra, based upon a Pushkin poem, the central character is a plainly masculine hussar, Vasily, who wants to get close to Parasha, whose mother has forbidden her to see him. With rather less suave artistry than Jupiter, he transforms himself into Mavra, a female cook, and wangles his way into the household in that disguise. All proceeds smoothly until a certain inevitable non-smoothness urgently needs attendance. Vasily takes advantage of the mother's absence to deal with it, but she returns unexpectedly...and catches him shaving!