How about you never actually meet the other player? The two of you can communicate, maybe by radio or something, but you never (or very rarely) actually see one another.
To take a setting from Dead Space and some tips from Amnesia: You're trapped on a space ship or station, and it has been attacked by some malevolent force. In order for the two of you to survive you're going to have to work together.
To take the Fatal Frame idea from above, there is some sort of artifact that can help you fight them off, but there is only one, and you have to pass it back and forth for various reasons - A hall infested with corrosive, evil matter, or needed to in order to solve a puzzle - to proceed.
That sound idea also comes into play, as what you say and what your friend says can be heard by monsters on both ends. Maybe a sequence occurs where one person with The Lamp - that is, the Artifact - has to solve a puzzle in a room that is filled with lots of precariously stacked metal bits or something, and has to be really careful not to knock anything over because his teammate is trapped in another room with a blind monster with really good hearing.
Monsters would take the Amnesia approach - They will tear you to bits in seconds if they catch you, so you don't want to see them, so they can't see you.
If one of you dies, then wither A: the match ends - you failed, B: The rest of the match becomes a super difficult one man challenge with an alternate route that one man could complete on his own, but be harder(monsters get more numerous, faster), or C: similar to B, except you can somehow revive the other player at checkpoints, so the alternate route is just a mad dash for the nearest checkpoint.
sorry bout wall o' text. just needed to get that all out there
-EDIT-
Dang, partially ninja'd
To take a setting from Dead Space and some tips from Amnesia: You're trapped on a space ship or station, and it has been attacked by some malevolent force. In order for the two of you to survive you're going to have to work together.
To take the Fatal Frame idea from above, there is some sort of artifact that can help you fight them off, but there is only one, and you have to pass it back and forth for various reasons - A hall infested with corrosive, evil matter, or needed to in order to solve a puzzle - to proceed.
That sound idea also comes into play, as what you say and what your friend says can be heard by monsters on both ends. Maybe a sequence occurs where one person with The Lamp - that is, the Artifact - has to solve a puzzle in a room that is filled with lots of precariously stacked metal bits or something, and has to be really careful not to knock anything over because his teammate is trapped in another room with a blind monster with really good hearing.
Monsters would take the Amnesia approach - They will tear you to bits in seconds if they catch you, so you don't want to see them, so they can't see you.
If one of you dies, then wither A: the match ends - you failed, B: The rest of the match becomes a super difficult one man challenge with an alternate route that one man could complete on his own, but be harder(monsters get more numerous, faster), or C: similar to B, except you can somehow revive the other player at checkpoints, so the alternate route is just a mad dash for the nearest checkpoint.
sorry bout wall o' text. just needed to get that all out there
-EDIT-
Dang, partially ninja'd