For lightning you want grounds as close to the building and strike points as possible. If you connect grounds together the lightning can go look for a better ground through your house and, as above per Lou, damage stuff in between.
In the event of step potential in the ground, which happens when grid people tie 3 phase 4 wire system neutrals to ground at different points (yeah it's a problem for utilities too) when you ground several points you are bridging the bad earth conductor with your conductor. When system faults happen cows get fried sometimes and your equipment will not handle that well either.
In the end the best combination is only one bonding point for your neutrals so that grounds do not carry any current ad develop voltage drops in them creating your own step potential problems. At the same time ground every piece of equipment to a standing plate in the floor around it (Think small Faraday cage)
I worked in grid protection schemes for 35 years and had to deal with this crap in theory and saw the ashes of faults many times. When a 230kV conductor faults to ground the ground at that point will be about 100kV to the rest of the world. Rings of step potential surround the fault point radiating outward for miles and miles. Telephone companies love this stuff. Demarcation points and equipment burns out miles away 'cause they conectin' the telephone lines from somebody else's ground to power lines and their own ground. Surprise!
As above the other side of the coin is to run a ground rod ring around your life, live in a Faraday cage and disconnect everything you have from ground. Let it float so there is no return path like bird on a wire.
I feel as if I am rambling here but I think Lou stated it quite well.
In the event of step potential in the ground, which happens when grid people tie 3 phase 4 wire system neutrals to ground at different points (yeah it's a problem for utilities too) when you ground several points you are bridging the bad earth conductor with your conductor. When system faults happen cows get fried sometimes and your equipment will not handle that well either.
In the end the best combination is only one bonding point for your neutrals so that grounds do not carry any current ad develop voltage drops in them creating your own step potential problems. At the same time ground every piece of equipment to a standing plate in the floor around it (Think small Faraday cage)
I worked in grid protection schemes for 35 years and had to deal with this crap in theory and saw the ashes of faults many times. When a 230kV conductor faults to ground the ground at that point will be about 100kV to the rest of the world. Rings of step potential surround the fault point radiating outward for miles and miles. Telephone companies love this stuff. Demarcation points and equipment burns out miles away 'cause they conectin' the telephone lines from somebody else's ground to power lines and their own ground. Surprise!
As above the other side of the coin is to run a ground rod ring around your life, live in a Faraday cage and disconnect everything you have from ground. Let it float so there is no return path like bird on a wire.
I feel as if I am rambling here but I think Lou stated it quite well.