We prove that a sequence of sets containing representatives of cupping partners for every nonzero ${\Delta^0_2}$ enumeration degree cannot have a ${\Delta^0_2}$ enumeration. We also prove that no subclass of the ${\Sigma^0_2}$ enumeration degrees containing the nonzero 3-c.e. enumeration degrees can be cupped to ${\mathbf{0}_e'}$ by a single incomplete ${\Sigma^0_2}$ enumeration degree.