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Abstract A phase shift in the acoustic oscillations of cosmic microwave background (CMB) spectra is a characteristic signature for the presence of non-photon radiation propagating differently from photons, even when the radiation couples to the Standard Model particles solely gravitationally. It is well-established that compared to the presence of free-streaming radiation, CMB spectra shift to higherℓ-modes in the presence of self-interacting non-photon radiation such as neutrinos and dark radiation. In this study, we further demonstrate that the scattering of non-photon radiation with dark matter can further amplify this phase shift. We show that when the energy density of the interacting radiation surpasses that of interacting dark matter around matter-radiation equality, the phase shift enhancement is proportional to the interacting dark matter abundance and remains insensitive to the radiation energy density. Given the presence of dark matter-radiation interaction, this additional phase shift emerges as a generic signature of models featuring an interacting dark sector or neutrino-dark matter scattering. Using neutrino-dark matter scattering as an example, we numerically calculate the amplified phase shift and offer an analytical interpretation of the result by modeling photon and neutrino perturbations with coupled harmonic oscillators. This framework also explains the phase shift contrast between self-interacting and free-streaming neutrinos. Fitting models with neutrino-dark matter or dark radiation-dark matter interactions to CMB and large-scale structure data, we validate the presence of the enhanced phase shift, affirmed by the linear dependence observed between the preferred regions of the sound horizon angleθ_sand interacting dark matter abundance. An increasedθ_sand a suppressed matter power spectrum is therefore a generic feature of models containing dark matter scattering with abundant dark radiation.