This code can only be entered if you have 2 SNES game controllers. Go to the options screen and press L, R, Start, Select, X, Y, A, and B quickly on your second controller. Use controller one to exit the options screen. Once your on the title screen, hold the L and R buttons and use the control pad to choose a stage.
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Passcodes
Use these passwords to select a level of choice in gameplay:

Level 2: Jafar, Abu, Jasmine, Genie
Level 3: Genie, Jafar, Aladdin, Abu
Level 4: Abu, Aladdin, Genie, Jasmine
Level 5: Jasmine, Jafar, Sultan, Jasmine
Level 6: Jafar, Jasmine, Aladdin, Jafar
Level 7: Aladdin, Jasmine, Abu, Sultan
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See the Special Ending
Finish the game with at least 70 red gems, and you'll get to see the Special Ending.