Can you mix eggshell paint to change the colour?

Yes, but remember that eggshell is already a changed color, so to speak. It's a colored white. Mix small amounts of the eggshell and other color to see your results. You may have to make several mixtures, so be sure to keep track of the amount of color you put into the eggshell so that when you get the color you want, you'll know how you got it and how to get it again.