© 2023 American Physical Society. The empirical spectra and E2 decay rates in Cd110,112,114,116 are shown to be consistent with a vibrational interpretation for low-lying normal states, coexisting with a single deformed ?-soft band of intruder states. The observed deviations from this paradigm show up in particular nonyrast states, which are properly described by a Hamiltonian with U(5) partial dynamical symmetry. The latter is characterized by a good (broken) symmetry in most (in selected) normal states, weakly coupled to intruder states.