Is it bad to have multiple grounding electrodes?
The grounded conductor is the white or gray Neutral. The Grounding conductor is the green or bare ground. The Grounded conductor is expected to carry current in normal service. The Grounding conductor only carries current in fault conditions.

For a (current/recent) detached structure they should be isolated all the way back to the single bond at the service entrance. That means removing any Neutral-Ground bond, and keeping all the neutral wires  on a neutral buss that is isolated from the case. Grounding conductors should all be connected to the case and the grounding conductor (which may be metallic conduit) leading back to the service entrance connection.

The detached structure should have one (or more) grounding electrodes. If it has a concrete slab or footing in direct contact with the soil, that should have a UFER ground installed when poured these days, but often that detail is forgotten.

My building has 5 ground rods and a 100 foot well casing as grounding electrodes. The more, the merrier. But when the next building goes up, the neutral and ground remain separated all the way back the first building. And the next one will actually have the (required, actually, in this state) Ufer Ground.