250.64(F)
To Electrode(s).
A grounding electrode conductor shall be permitted to be run to any convenient grounding electrode available in the grounding electrode system or to one or more grounding electrode(s) individually
Basically you can run your GECs any way you want to, to create your grounding electrode system.
The handbook shows a nice picture of this in Exhibit 250.27. It has a GEC going from your service, to the cold water, then from a different section of the cold water it goes to building steel. From a different section of building steel it goes to a ground rod. Another section of the building steel attaches to the ufer. And another section of the building steel attaches to a ground ring.
As long as you don't use the provisions for smaller GECs like a ground rod while feeding your cold water you can do it anyway you want.
Except however, if the E.E. on your plans calls out for seperate runs from the service which they almost always do in commercial.
