Of the three properties of color, value, hue, and, intensity, intensity is the least understood. It is often confused with value. That, though, is another discussion. Here I will address my personal approach to adjusting intensity, both up (increased saturation and brilliance of color) and down (decreased saturation and chroma). Consider yellow ochre: it's intensity is easily raised by adding cadmium yellow and lowered by adding almost anything else. Well, right there is the secret of lowering intensity. It is accomplished when almost any pigment, other than a brighter version of its same hue family, is mixed with it. This fact explains the abundance of muddy and chalky (and unsuccessful!) paintings we all have as we set off on our painting journey.
Back to the issue at hand. How I lower intensity depends on what I am after. I might lower the intensity of cadmium yellow, for instance, with burnt sienna where I want a warm darker lower intensity, with dioxazine purple where I want to preserve yellowness as much as possible, with white or a white and black mix where I need the yellow to be duller but stay in high value, with black when I don't mind a bit of a green slant, and with miscellaneous neutrals mixed on the palette when I simply wish to subdue the color. Summed up, I lower intensity by adding an analogous but duller pigment, adding the hue's complement, adding white, adding gray, adding black, and by adding neutral mixes.I have experimented with premixing neutrals. This can be exciting to explore. Empty tubes can be purchased though expensive, or toothpaste tubes repurposed. Somehow, though, I end up using the same trusty cast of characters on my palette and then go from there.
Check out my book The Painter's Workbook: A Self-Study Guide for Becoming a Better Painter for exercises and a thorough discussion of intensity.