Decay properties of multiphonon quadrupole vibrational states and intruder structures in ${}^{116}\mathrm{Cd}$ have been examined with the ${(n,n}^{\prime }\gamma )$ reaction. γ-ray excitation functions, angular distributions, and $\gamma -\gamma$ coincidences have been measured. Lifetimes of many levels were determined with the Doppler-shift attenuation method, exposing the degree of collectivity of the intruder structure and the three-phonon states. In combination with other recent results, this new information reveals that the intruder picture is well supported in the Cd nuclei. However, a puzzle not present in the lighter Cd nuclei emerges in ${}^{116}\mathrm{Cd};$ strong configuration mixing between intruder and multiphonon vibrational excitations cannot describe the observed decays of the lowest $0^{+}$ excited states.