There may have been more than one signed copy of this contract, and another copy may have been countersigned. If so, would it not be a binding contract?
Yes, another fully executed copy would be a valid contract, Back in the days before Xerox machines, they would either be re-typed or done with carbon paper, but in the case of a pre-printed form like this, it would not be necessary to do anything but make the same changes as the original.
But, typically, all copies get signed at the same time, so that all parties have a copy of the fully executed agreement. Otherwise, you are looking for trouble down the road if a dispute arises over whether it was ever fully executed, or whether one of the parties signed it at a later time.