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You aren't limited to that for the whole entire game - the palettes can be changed at pretty much any point. But there are two of them, they have 3 colours each, and they are sourced from the only 4 colours you'll be using for the entire game.

With that said, there are games which put one sprite on top of another and achieve all 4 colours. So if you're not spamming sprites you can probably get away with 4+transp.