The developer of Back 4 Blood, Turtle Rock Studios, has confirmed the game will not have a campaign versus mode.
In an FAQ thread in the studio’s official Discord server, it stated: “We do not have plans to have a campaign versus mode at this time”.
Back 4 Blood does have a versus mode, allowing two teams to take it in turns to fight each other as the Cleaners and the Ridden. But there is no campaign level akin to Left 4 Dead, where players would have to fight through player-controlled zombies to get to the safe house.