Excavation Technique
Demonstrate (When you cast this spell, you may copy it. If you do, choose an opponent to also copy it. Players may choose new targets for their copies.) Destroy target nonland permanent. Its controller creates two Treasure tokens.
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Official rulings (5) · Scryfall
If the spell requires targets, you choose the target of the original spell as you cast it. If you create a copy of the spell, you may choose new targets for the copy as you create that copy. Similarly, the opponent you chose to create a copy may choose new targets for that copy as it’s created. In other words, your opponent will know the targets of your original spell and your copy when choosing the new targets, if any, for their copy.
This means that if you cast a spell with demonstrate and both you and an opponent copy it, the opponent’s copy will resolve first, then your copy will resolve, and finally the original spell will resolve.
If you copy a spell with demonstrate, you then immediately choose an opponent. If they copy the spell, it goes on top of the stack.
You choose whether to make a copy as the demonstrate ability resolves. This happens before the original spell resolves. Your copy goes on the stack above the original spell.
If you cast the spell and choose not to copy it, no opponent will get to copy it either.