You could actually get more than 4096 colors. One of the popular 3D computer graphics programs for the Amiga used assembly language and interrupts to swap the

You could actually get more than 4096 colors. One of the popular 3D computer graphics programs for the Amiga used assembly language and interrupts to swap the colors available on the fly (per scan line I think) which allowed for smooth shading of graphics with a much greater range of colors. I'm not sure if any other software developers ever figured out that trick though, which was embedded in the viewer software for animations.