If you obtain a grade AA (9500000 pts+) in the Expert difficulty on the final stage of your credit, you will advance to the Extra Stage. This does not work on Tutorial, Nonstop or Challenge modes, or on Battle mode. In the Extra stage, you must play on expert difficulty with these options: 1.5x, Reverse, Rainbow, and Pressure Gauge, which makes your lifebar start at full but also prevents you from recovering energy.
Depending on the difficulty you chose, you may be presented with a "boss" song to play for your Extra Stage. If you successfully pass this song, you may then play the One More Extra Stage. For OMES, you must play the hidden song "Chaos" on Expert difficulty, with no options, and on Sudden Death, where you fail instantly if you obtain even a single judgement of Good, Almost, Boo or N.G.
Easy mode has no boss song, so you cannot access the OMES on this mode.