Adding 3 colors would make it base 5 (BW+rgb) and give log(5)/log(2) or about 2.3 times the information per dot.
2 dots at 2 possibilities each gives 4 (2^2)
They only diverge from there. Or am I doing my math wrong?
Log(25)/log(4) is 2.3. Among other things this definition has the nice property that two disks/pages/drives/bits together contain the sum of the capacities instead of their product.