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In order to unlock more levels, you need to play through the game in either Arcade or Ranking mode. Stage mode only allows you to replay levels you've unlocked through those other two modes.
When you choose either Arcade or Ranking mode, it will ask you to choose between Normal and Extreme. Beating a stage in either of these modes unlock them in Stage mode.
In order to get those other stages on the grid (3B, 4B, etc.) you need to perform well in Arcade or Ranking mode. For example, if you accumulate enough points in Stage 2, you'll be offered a choice between playing Stage 3A or 3B after you beat the boss.