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Analogous to electromagnetic bianisotropy, engineered piezoelectric metamaterials can possess electro-momentum coupling between the macroscopic momentum and electric stimuli. This indicates the applicability of piezoelectric metamaterials for wave scattering with an extra design degree of freedom, in the same way as acoustic materials with Willis coupling between the macroscopic momentum and strain. To fully utilize this novel bianisotropy, we derive for the first time tight theoretical bounds on the effect of electro-momentum coupling on scatterers based on energy conservation and combining two acoustic and electromagnetic polarizability tensors to analyze passive bianisotropic scatterers under both acoustic and electromagnetic waves. Our derived bounds are verified by comparing them with analytical scattering solutions. Results show that the bianisotropic scattering performance can be of the same order as the non-bianisotropic terms via the aid of electro-momentum coupling, even for simple designs with small Willis coupling. We further reveal the possibility of utilizing electro-momentum coupling for tunable scattering-cloaking applications of the subwavelength-sized scatterers. This sheds light on the promising potential of piezoelectric metamaterials for tunable scattering devices in which bianisotropy can be modulated by external electric stimuli.