If a Vesuvan Doppelganger is in play having assumed the characteristics of, say, a Royal Assassin, would cloning the Doppelganger at this point be tantamount to having cast a second Doppelganger? (...that could then change into something else next turn, after spending a turn as another Royal Assassin, but with summoning sickness?)
The Clone would enter the battlefield as a copy of whatever Vesuvian Doppelganger is cloning, with the Doppelganger's extra ability. In fact, the rules about copying objects have an example covering this specific scenario
The copy’s copiable values become the copied information, as modified by the copy’s status (see rule 110.6). Objects that copy the object will use the new copiable values.
Example: Vesuvan Doppelganger reads, "You may have Vesuvan Doppelganger enter the battlefield as a copy of any creature on the battlefield except it doesn’t copy that creature’s color and it gains ‘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. If you do, this creature gains this ability.’" A Vesuvan Doppelganger enters the battlefield as a copy of Runeclaw Bear (a 2/2 green Bear creature with no abilities). Then a Clone enters the battlefield as a copy of the Doppelganger. The Clone is a 2/2 blue Bear named Runeclaw Bear that has the Doppelganger’s upkeep-triggered ability.