Well, for people who consider that to not be a violation of 250.6 I will just reiterate my disagreement. (Mind you, I know that sometimes there is objectionable current on water pipes between houses, but that's something people don't really have knowledge or control of if they comply with using the water pipe as an electrode, so it is what it is.)
If you're complying with 250.50, there's generally no reason to run multiple GECs, especially with a single service disconnecting means.
Here's my concise response to the OP's post:
Not only can you, but you should. You're more likely violating code and good grounding practices if you do it some other way.