American illustrator Andrew Loomis in Creative Illustration (1947) recommends a method called “toning” the palette or spectrum. The way you do it is to choose a single color and mix it into all the other colors on the palette. The amount of this toning color can be a little or a lot depending on how subtle you want the effect to be.
In this set of samples, clockwise from upper left, he has toned the colors with red, blue, green and orange. The addition of a single color to the colors on the palette cuts back on the saturation of all the other colors, the toning color staying the same.
It would be a good exercise to try this method as a set of adjacent experiments, as Loomis has done. Side by side the color keys are obvious; alone it can be hard to see the effect. Note, too, that Loomis has chosen to feature his toning color prominently in the dress or the background. He doesn’t say this, but I would recommend that you tone the white with the theme color as well, because white sets the key for any color scheme.
More Loomis online, link.