Let's say that I cast Goblin Grenade, sacrificing a goblin to pay it's additional cost. Then, before it resolves I cast Increasing Vengeance, which allows me to copy the Goblin Grenade. Since I've already paid the additional cost of Goblin Grenade, do I have to pay it again?
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You don't need to sacrifice another Goblin or pay any other costs.
Additional costs are paid as part of casting a spell. When you copy a spell with Increasing Vengeance, the copy just pops into existence straight on the stack. Technically speaking, it's never "cast" at all.