Sorry Gloat, but you're not entirely right here.
Indeed, the answer is No.
But it's not because you can only use the key once for one install.
It is, because it would violate the End User License Agreement. The rules state that you may only use this game for one player, on one pc. This is for piracy reasons, obviously.
But, there is one exception.
If you want to use the game on a second pc to be able to create a dedicated multiplayer server, you are allowed to install it on a second pc.
But!
You may not use that second installment to play. So you may play on your main pc, and the server application runs on the second pc.
If a familiymember or friend would be playing along with you, and you would get caught like that on one of the servers, you risk getting banned from both MP and the forum.
So, you may only PLAY the game on one pc, for one user. (Of course a friend you may have over, may play on this one pc too, if you take turns. But you are responsible for your account at all times.)
Hope that clears things up!
And welcome to the forums btw, gjmonaco!!
Regards,
Fred