I don´t know what software you are using, but in case you have Photoshop CS4 or newer, you could also try with the "vibrance" tool instead of saturation. This way the saturated red will be affected more, with less variation in the other colors.
Again, if using Photoshop, you could also use Softproofing, with sRGB as output color space and then turn on gamut warning. This will let you adjust vibrance or saturation just enough to avoid clipping any color.