If you have one warlock / hunter / titan and you completed a raid, then go the same class but different character, do you not get loot from the raid.
Say;
Crown of Sorrow: Warlock 1 (loot)
Crown of Sorrow: Warlock 2 (loot or no loot)
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You only earn powerful rewards and raid drops once per character class per week. There is no benefit for running multiple of the same class.