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Magnetoacoustic tomography with magnetic induction (MAT-MI) is an imaging approach proposed to conduct noninvasive electrical conductivity imaging of biological tissue with high spatial resolution. In the present study, based on the analysis of the relationship between the conductivity distribution and the generated MAT-MI acoustic source, we propose a new multi-excitation MAT-MI approach and the corresponding reconstruction algorithms. In the proposed method, multiple magnetic excitations using different coil configurations are employed and ultrasound measurements corresponding to each excitation are collected to derive the conductivity distribution inside the sample. A modified reconstruction algorithm is also proposed for the multi-excitation MAT-MI imaging approach when only limited bandwidth acoustic measurements are available. Computer simulation and phantom experiment studies have been done to demonstrate the merits of the proposed method. It is shown that if unlimited bandwidth acoustic data is available, we can accurately reconstruct the internal conductivity contrast of an object using the proposed method. With limited bandwidth data and the use of the modified algorithm we can reconstruct the relative conductivity contrast of an object instead of only boundaries at the conductivity heterogeneity. Benefits that come with this new method include better differentiation of tissue types with conductivity contrast using the MAT-MI approach, specifically for potential breast cancer screening application in the future.