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The swap Monte Carlo algorithm allows the preparation of highly stable glassy configurations for a number of glass-formers but is inefficient for some models, such as the much studied binary Kob–Andersen (KA) mixture. We have recently developed generalizations to the KA model where swap can be very effective. Here, we show that these models can, in turn, be used to considerably enhance the stability of glassy configurations in the original KA model at no computational cost. We successfully develop several numerical strategies both in and out of equilibrium to achieve this goal and show how to optimize them. We provide several physical measurements indicating that the proposed algorithms considerably enhance mechanical and thermodynamic stability in the KA model, including a transition toward brittle yielding behavior. Our results thus pave the way for future studies of stable glasses using the KA model.