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While an instant or sorcery spell that you control is on the Stack, you can choose to exile that spell instead of waiting for it to resolve. If you do, then Nivmagus Elemental gets two +1/+1 counters.
After casting the spell, you get two choices. 1: Wait for the spell to resolve, and get its effect. OR 2: Exile the spell (it won't resolve if it gets exiled), then put two +1/+1 counters on Nivmagus Elemental
When an instant or sorcery is cast, it goes on the stack. Nivmagus Elemental allows you to exile that spell off of the stack, placing two +1/+1 counters on it. The spell that was exiled will not resolve, meaning any effects from it will not happen.
Whenever you "cast" a card it is placed on the "stack". while a card is on the stack it is considered a "spell". It is at this point that you can activate the ability of Nivmagus Elemental .
So while Nivmagus Elemental is on the field in your control you can cast, say, Unsummon from your hand. Before the spell resolves you announce that you will activate Nivmagus Elemental . Unsummon exiles, Nivmagus Elemental gets stronger, and Unsummon does nothing.
You can keep doing this as long as you have enough mana to cast more spells.
I was considering something else entirely. I would want to keep Unsummon for my opponents stuff. I was thinking more along the lines of how an opponent may respond to Barter in Blood when you cast it to get effects from their creatures before they are forced to sac them. if they do so, you may exile the Barter in Blood to add the counters and get overall value out of the card when your opponent may think they have the one up on you.
I also considered the option of Reverberate or Dual Casting , which would allow you to cast a spell like Pillar of Flame , and exile it if you have no real targets. Leaning more towards the application of Dual Casting on Blistercoil Weird . if you cast something, you can untap the Blistercoil Weird have the original resolve, but exile the copy of the instant/sorcery which goes on the stack. You copy the spell before it resolves. The optimal spell I haven't given it much thought, but it could work with atleast afew things while making that Nivmagus Elemental a fatty.
Once a spell has started resolving no one gets priority until it has finished resolving. And players can only cast spells or activate activated abilities when they have priority.
Also you cannot cast a spell that uses the keyword "target" whel there is no legal target.
On a side note, I believe the optimal spell you are searching for is Epic Experiment .
I don't think he mean 'after it has started to resolve'. I think he means that if his opponents sacrifice their creatures to something else in response to him casting Barter in Blood , he could then exile the Barter in Blood , so that he does not have to sacrifice his own creatures, which is perfectly legal.
@Rayenous Thank you for clarifying, I'm not sure what I said to misconstrue my point, but I dont think I have faced an opponent who will just say, "Ok, my i will sacrifice my creatures instead of taking advantage of another ability." I meant it to force an ability as to lure my opponent into a false sense of security, for example if an opponent has a Griselbrand and a golgari guildmage out on the field, and I play Barter in Blood , hes going to sac a 7/7 to make seven creature tokens instead of just eating the Griselbrand . Not the best of examples, but the only one i can think of at the moment.