You want to play Metro 2033 Redux (the first game) in co-op. Scenario B: You are actually looking to play Metro: Last Light (or the DLC Chronicles Pack ) in co-op.
: There are RTS-style mods that recreate Metro stations and units for tactical multiplayer battles. The State of Official Multiplayer No Rage Against The Dying Of Metro 2's Multiplayer Light metro 2033 coop mod
While you cannot play the original story in co-op, fans have explored these alternatives to get their multiplayer fix: You want to play Metro 2033 Redux (the first game) in co-op