In reality, artists often use different base colors anyway. One way to do it is to have 2 versions of the base colors, one warm, one cold. The reason is that for example a greenish blue like Cyan would make it harder to mix vivid violets (by adding a red on the other direction of the color wheel). So you use a greenish blue (Cyan) and a redish blue (e.g. Aquamarine), a blueish red (e.g. Magenta) and a yellow-ish red, and so on.