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Whenever another creature enters, 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 first one gets the second one's triggered ability, so it will copy the next creature that enters twice. It will only do so the next time a creature enters, because the second "becomes a copy" effect to resolve will erase the extra triggered ability.