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We perform a high-resolution cosmological zoom-in simulation of a Milky Way (MW)--like system, which includes a realistic Large Magellanic Cloud analog, using a large differential elastic dark matter self-interaction cross section that reaches $\approx 100~\mathrm{cm}^2\ \mathrm{g}^{-1}$ at relative velocities of $\approx 10~\mathrm{km\ s}^{-1}$, motivated by the diverse and orbitally dependent central densities of dwarf galaxies within and surrounding the MW.
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