Abstract Self-interacting dark matter (SIDM) is increasingly studied as a potential solution to small-scale discrepancies between simulations of cold dark matter (CDM) and observations. We examine a physically motivated two-state SIDM model with both elastic and inelastic scatterings. In particular, endothermic, exothermic, and elastic scattering have equal transfer cross sections at high relative velocities (vrel ≳ 400 km s−1). In a suite of cosmological zoom-in simulation of Milky Way-size haloes, we vary the primordial state fractions to understand the impact of inelastic dark matter self-interactions on halo structure and evolution. In particular, we test how the initial conditions impact the present-day properties of dark matter haloes. Depending on the primordial state fraction, scattering reactions will be dominated by either exothermic or endothermic effects for high and low initial excited state fractions respectively. We find that increasing the initial excited fraction reduces the mass of the main halo, as well as the number of subhaloes on all mass scales. The main haloes are cored, with lower inner densities and higher outer densities compared with CDM. Additionally, we find that the shape of the main halo becomes more spherical the higher the initial excited state fraction is. Finally, we show that the number of satellites steadily decreases with initial excited state fraction across all satellite masses.