We then delve into the analysis of core-ionization convergence within successive embedding spaces. Our findings reveal that the nearest neighbor in the embedding space provides accurate core-ionization results, exhibiting a systematic deviation of 0.1 eV compared to unembedded values. This approach offers computational acceleration of 2-3 orders of magnitude. Additionally, we demonstrate the applicability of the high-level EOM-CC method with DMET in computing core-ionization for extended systems such as uracil-hexamer, azafullerene, and chlorophyll a molecules.