Both plays start with a shipwreck that takes characters to another world, so to speak. Viola shipwrecks in Illyria and must become accustomed to a new identity and new people in order to survive there on her own as a woman without male protection. Ferdinand and his entourage shipwreck on Prospero's island and become chess pawns in his game for power.
Both plays end with a reconciliation between parties, but there are tinges of the bittersweet in both as well. Malvolio swears revenge on all the characters in his last scene. The Tempest ends with Prospero giving up his magic (which one may see as a good or bad thing, depending upon one's reading of the character), thus signaling an exit from the island's otherworldly enchantment and a return to ordinary life.
Both plays also boast metafictional elements. Twelfth Night features many characters "playing" roles: Viola becomes Cesario to survive in a male-dominated world and even "plays" Orsino to an extent when she tries to woo Olivia for him....
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