Grounding at multiple points?

Not necessarily. I shifted this to Tinkering where folks who know such stuff hang out.

Single-point grounding also limits the ground loops that occur when more than one conductive path exists between two points. If the electrical equipment is not only bonded to ground bars, as in Figure 1, but to various building steel columns—if available—and if the grounding potential is different in the building due to an electrical storm, on a multi-point grounding system, noise could circulate, cause error in equipment operation and become difficult to isolate.

Source.

Connecting two ground points with different grounding potentials will necessarily create a current between them. Just ground to the best one in my opinion.