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Whenever another creature enters the battlefield, Unstable Shapeshifter becomes a copy of that creature, except it has this ability.
If an Unstable Shapeshifter is on the battlefield when another Unstable Shapeshifter enters the battlefield, the first one gets the second one’s triggered ability, so will copy the next creature that enters the battlefield twice. It will only do so the next time a creature enters the battlefield, because the second “becomes a copy” effect to resolve will erase the extra triggered ability.