If the generator has the neutral bonded to "ground" in the generator and a switched neutral is employed in the transfer switch ( as it should be with a bonded generator neutral), a ground electrode should not be used or needed because the neutral is still bonded to ground through the generator.. Doing anything else may cause circulating currents in the grounding / bonding conductors and will defeat the purpose of the switched neutral in the transfer switch.
A.D
The ground cable may be grounded multiple points anywhere (or everywhere) on that ground wire. Grounding the generator with a separate grounding electrode is no different than any other supplementary ground with this respect. The key to a safe configuration is that the neutral must be bonded at one and only one point in the electrical system. So long as the neutral is switched in the transfer switch, there will be no circulating current on the ground.
Even if you make no bond at the portably genny, you still have an incidental ground where the chassis sits on the earth. Depending on the design of the chassis, the total surface area of incidental ground might even approach that of an 8' ground rod, which could create a dangerous condition, given that this ground connection is easily broken. Safest thing to do is drive another rod.
Per 250.30(3), if you do share a GEC between the portable genny and the normal service, it has to follow the same rules as the GEC normally does from the panel to the rod. EG, big wire, no breaks without exothermic welds, etc. Hard to do with a cord & plug.
