No, but a material is usually a color plus some other settings, so a library of colors is mostly what you need.
Interesting question! Usually, we think of a specular reflection as being mirror-like, so that the reflected light is the same as the incoming light. So a red spotlight on a shiny green sequin reflects as red light.
But, you don't need to do that. Maybe you have something a little less shiny than the sequin, but still reflective. (Satin?) Maybe it contributes a bit of color, so that the specular reflection is a combination of its color and the light's color.
You can do that in the Phong model, but having a non-white color as the specular color.
Note that the combination is multiplication, not addition, so red+green=yellow but red*green=(1,0,0)*(0,1,0)=black. But yellow*cyan=(1,1,0)*(0,1,1)=green.