From detailed spectroscopy of ^{110}Cd and ^{112}Cd following the β^{+}/electron-capture decay of ^{110,112}In and the β^{-} decay of ^{112}Ag, very weak decay branches from nonyrast states are observed. The transition rates determined from the measured branching ratios and level lifetimes obtained with the Doppler-shift attenuation method following inelastic neutron scattering reveal collective enhancements that are suggestive of a series of rotational bands. In ^{110}Cd, a γ band built on the shape-coexisting intruder configuration is suggested. For ^{112}Cd, the 2^{+} and 3^{+} intruder γ-band members are suggested, the 0_{3}^{+} band is extended to spin 4^{+}, and the 0_{4}^{+} band is identified. The results are interpreted using beyond-mean-field calculations employing the symmetry conserving configuration mixing method with the Gogny D1S energy density functional and with the suggestion that the Cd isotopes exhibit multiple shape coexistence.