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From The PSUPedia
Partner missions are unique missions that require at least two players to initiate and complete. In essence, they are identical to party missions in that a party must be formed before the mission can be accepted, party member incapacitation will lead to immediate failure and the departure of a team member or change of party leader will automatically abandon the mission. There are two points that set partner missions aside from party missions, however. First, starting at difficulty S, party missions offer a randomized lottery of rewards for clearing the mission with a grade of S. Partner missions only offer one predetermined prize. The second point that sets these missions apart is that they are not part of the upcoming time attack ranking system known as GUARDIANS Limit Attack.