You may have Vesuvan Doppelganger enter as a copy of any creature on the battlefield, except it doesn't copy that creature's color and it has "At the beginning of your upkeep, you may have this creature become a copy of target creature, except it doesn't copy that creature's color and it has this ability."
Upon summoning, Doppelganger acquires all characteristics except color of any one creature in play on either side; any creature enchantments on the original creature are not copied. During controller's upkeep, Doppelganger may take on the characteristics of a different creature in play instead. Doppelganger may continue to copy a creature even after that creature leaves play, but if it switches it won't be able to switch back.
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