Here's examples of games with 4 colors
You can only have absolutely 4 colors at any time
You can make original Game Boy games display more than four colours on static 8x8 areas of the screen with Super Game Boy (SNES).
Here are a few examples:
none of those examples have more than four colours in an 8x8 area of the gameboy screen though, only in the SGB border. Still, I think including an SGB style border for future GBJAM entries might be a really cool idea!
What I meant to say is that you can change the 4 color palettes of the static 8x8 sections of the Game Boy screen to allow the game to display more than 4 colors on the screen when used with Super Game Boy, but the 8x8 tiles still display 4 colors each.