There was something similar to what you suggest in XCom 2. Squad members who went on missions together, and had compatible personalities, gradually increased their bonding, until a threshold was met and they "Bonded". This enabled additional perks, like an extra move through teamwork. Over time, the level of the bond could be increased, to unlock further, enhanced perks. If a bondmate was injured severly or died, it had a chance to trigger a reaction in the other member, including "going berserk"! It was an enjoyable part of the game.
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Fallout 4 did this sort of thing too, though it's been long enough that I don't quite recall the exact details...
