There are blend colors and hue correct nodes that'll do what you are looking for. But their values would be to be changed via expression or render time attribute.
There are many many different ways to achieve what I believe you are looking for. The easiest for this example would just be to do it with an animated gradient texture running into a blend node (or even skip the blend node and have your texture going everything).
The render time attributes would be the way I would do it, but you wouldn't be able to see the result in the viewport.
You can also probably do this with mash and an offset node (but I hate rendering mash colors).
