[amluto]

> Adding a second grounding rod anywhere else would violate code in most states and potentially create a grounding loop and fire hazard.

Can you cite the relevant portion of the code? Or, for that matter, can you explain why exactly a ground loop is a fire hazard? If this was a hazard, then buildings would burn down when a grounded metallic conduit was buried underground (perfectly legal and very common, although dubiously wise if the conduit is galvanized steel), when anything conductive and connected to building ground (an outdoor appliance, a person touching a switch, etc) touched the ground, or in any building with an associated ordinary in ground swimming pool (which is extensively bonded and generally grounded at the pool equipment pad).

Now you do need to avoid connecting neutral to ground in more than one place if you are a modern NEC-following project or a utility in California, for quite good reasons, but those reasons aren’t a “ground loop” or really a fire hazard — it’s because intentionally running current through a circuit that parallels a path through ground will make a fraction of that current flow through the ground, with potentially unfortunate consequences.

[dpifke]

Multiple grounding rods (electrodes) are permitted by § 250.52, but they have to be bonded together and kept away from other (non-bonded) grounding systems:

Electrode Spacing. Where more than one of the electrodes of the type specified in 250.52(A)(5) or (A)(7) are used, each electrode of one grounding system (including that used for strike termination devices) shall not be less than 1.83 m (6 ft) from any other electrode of another grounding system. Two or more grounding electrodes that are bonded together shall be considered a single grounding electrode system.

http://thenecwiki.com/2021/02/article-250/

That said, it would be very strange to add another grounding rod just because you added another breaker or outlet—I can't think of any circumstance where that would be required, unless the existing service entrance was not properly grounded, in which case you have bigger problems.

[amluto]

That section AIUI is about “grounding electrodes” that are intended for use as part of the required main ground. NEC 250.54 says you may install an auxiliary grounding electrode if you are so inclined without following all those rules. Other sections of the NEC explicitly allow burying things like rigid metallic conduit underground, which is a lot like a grounding rod attached to a branch circuit or feeder.