We perform for the first time high-resolution zoom-in re-simulations of individual halos in the context of the Multi-coupled Dark Energy (McDE) scenario, which is characterised by the existence of two distinct dark matter particle species with opposite couplings to a Dark Energy scalar field. We compare the structural properties of the simulated halos to the standard Lambda-CDM results. The zoomed-in initial conditions are set up using a specifically designed code called ZInCo that we publicly release along with the present paper. Our numerical results allow to investigate in detail and with unprecedented resolution the halo segregation process that characterises McDE cosmologies from its very early stages. In particular, we find that in contrast to what could be inferred from previous numerical analysis at lower resolution, the segregation process is already in place at redshifts as high as z ~ 7. Most remarkably, we find that the subsequent evolution of the segregation leads to the formation of cored total matter density profiles with a core size that progressively increases in time. The shape of the cored profiles can be accurately predicted as the superposition of two NFW profiles with an increasing offset, thereby confirming the interpretation of the simulations results in terms of the segregation of the two dark matter components of the halo as a consequence of their different coupling to the Dark Energy field.
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