Self-interacting dark matter (SIDM) models offer one way to reconcile inconsistencies between observations and predictions from collisionless cold dark matter (CDM) models on dwarf-galaxy scales. In order to incorporate the effects of both baryonic and SIDM interactions, we study a suite of cosmological-baryonic simulations of Milky-Way (MW)-mass galaxies from the Feedback in Realistic Environments (FIRE-2) project where we vary the SIDM self-interaction cross-section $sigma/m$. We compare the shape of the main dark matter (DM) halo at redshift $z=0$ predicted by SIDM simulations (at $sigma/m=0.1$, $1$, and $10$ cm$^2$ g$^{-1}$) with CDM simulations using the same initial conditions. In the presence of baryonic feedback effects, we find that SIDM models do not produce the large differences in the inner structure of MW-mass galaxies predicted by SIDM-only models. However, we do find that the radius where the shape of the total mass distribution begins to differ from that of the stellar mass distribution is dependent on $sigma/m$. This transition could potentially be used to set limits on the SIDM cross-section in the MW.
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