[en] We propose to observe the enhanced Casimir repulsion between two parallel multilayer walls made of alternating layers of a topological insulator (TI) and a normal insulator. Based on the transfer matrix method, the Fresnel coefficients matrix is generalized to apply to the TI multilayer structure. The Casimir repulsion under the influence of the magnetization orientation in the magnetic coatings on TI layer surfaces, the layer thicknesses, and the topological magnetoelectric polarizability, is investigated. We show that, for the multilayer structures with parallel magnetization on the TI layer surfaces, it is possible to enhance the repulsion by increasing the TI layer number, which is due to the accumulation of the contribution to the repulsion from the polarization rotation effect occurring on each TI layer surface. Generally, in the distance region where there is Casimir attraction between semi-infinite TIs, the force may turn into repulsion in TI multilayer structure, and in the region of repulsion for semi-infinite TI, the repulsive force can be enhanced in magnitude, the enhancement tends to a maximum while the structure contains sufficiently many layers. - Highlights: • Enhancement of Casimir repulsion for topological insulator (TI) multilayers is shown. • Fresnel coefficients matrix is generalized to apply to the TI multilayer structure. • Multilayer with parallel magnetization on TI surfaces is needed for the enhancement. • Enhancement is due to accumulation of polarization rotation effect on TI surfaces.