You can definitely do that with computers. However, each computer needs to have the custom campaign installed.
Er, unless you're talking about Cold Stream, which is an "officially-sponsored" community map that was patched into each game. But if its something from l4dmaps, for example, then each one has to have it.
Custom maps are pretty awesome! They extended the replay value of the game soooo dramatically. Even the really s****y ones are still fun to play with friends sometimes.
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You have no time to ponder such questions, as Link has just grabbed a Smash Ball.
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