Without knowing if its a technical limitation due to how the painting data is stored, or if its just a design choice to limit the palette to 11 options (12 if you include storing transparency), I'm going to assume the texture storage has the capability of storing the per pixel data in at least 4 bits (16 options - 15 colours + transparency)
Current Palette:

(#1) I can see that there has been a previous request for a shade of grey to be added. I would actually suggest at least two shades of grey. So we have a monochrome ladder from Black, Dark Grey, Medium Grey, White. Dithering between these 4 would give us a good variety of neutral tones across the brightness spectrum, but on their own can be dithered with the other pigments to lighten or darken them in different ways. Greys also have a special ability to take on the hue of neighbouring pixels. I've included some 'warm' greys that are a little higher on the red spectrum.
(#2) Adjust existing hues/saturations/brightness:
- Red and Orange are currently almost the same both in saturation and hue.
- I would suggest shifting the red by upping the brightness, and hue more towards blue to give more of a pink tint.
- For orange desaturate a little. I would then darken the purple as it would be too close to the new red.
- Darken the blue to allow for two shades of blue.
- Slightly desaturate the yellow.
(#3) Round out the palette to 15 colours with:
- Dark Green,
- Medium Brown,
- Bone/Skin Tone,
- Medium-Light Blue.
Perhaps a Credo completion is required to unlock these final 4?
Here is a visual guide of what I am suggesting/requesting and some examples of why just a few adjustments and a handful of extra colours can make a world of difference for the art we can make and place in the world:
