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Abstract Earth's accretion was highly energetic and likely involved multiple global melting events. Following the Moon‐forming giant impact, extensive mantle melting and the separation of solids and melts under deep mantle pressures likely produced a basal magma ocean (BMO) beneath the solidified mantle. The presence and evolution of the BMO have been proposed to explain key geophysical and geochemical features of the lowermost mantle. Understanding the evolution of the BMO is crucial for testing these hypotheses, but its interaction with the core presents a significant challenge, as the mechanism of this exchange remains unclear. In this study, we develop a theoretical framework to assess the regime of BMO‐core exchange based on the compositions of the BMO and the core. We propose that during solidification, the BMO may evolve into a regime where the reaction at the BMO‐core interface drives compositional convection in liquids on both sides, if the core has a high enough Si content (–, under the assumption that the O content is –). In this scenario, the BMO‐core exchange would be much more efficient than previously estimated, buffering the tendency of FeO enrichment during crystallization and shortening the lifetime of the BMO.