I do a lot of LAN gaming with my friends. Generally games allow you to play LAN without online authentication (ie, Unreal) so I can use the same copy on all of my computers (this isn't really piracy since they are all my computers). However, this has the drawback that if I start a server, people on the internet can't connect. To be able to connect to it, I would have to set up an online (not just a LAN) server. This requires a full copy of the game on each computer. Does steam allow me to buy slots for each game? Like I buy one copy of Battlefield 3, then pay for additional licenses to play off the same account at the same time, but on a different computer? I don't want to maintain 5 different accounts for 5 different computers.
You cannot log onto the same Steam account in multiple places or it will kick other computers off. Additionally, I think you are unable to 'double buy' a game (though if you got the same game different ways—in a pack and a la carte, for example—you might) on the same account unless it's a gift.
However, you may be able to launch Battlefield outside of Steam (look in the
steamapps folder for the executable) however, and work from there. As you suggest, playing online with the same copy may not work, but a LAN game may. Using one copy on multiple computers simultaneously is a little grey though.
Steam cannot be opened from more than 1 computers when you are online. If you try to connect from another computer, your first session will be closed.
You cannot open one Steam account from more than one computer; all other instances would be logged out.
There is a workaround, though: if you can run a game via LAN, you'll also be able to run it via a VPN or some other, similar mechanism. Try using Hamachi.