Inhibitors that bind competitively to the ATP binding pocket in the kinase domain of the oncogenic fusion protein BCR-Abl1 are used successfully in targeted therapy of chronic myeloid leukemia (CML). Such inhibitors provided the first proof of concept that kinase inhibition can succeed in a clinical setting. However, emergence of drug resistance and dose-dependent toxicities limit the effectiveness of these drugs. Therefore, treatment with a combination of drugs without overlapping resistance mechanisms appears to be an appropriate strategy. In the present work, we explore the effectiveness of combination therapies of the recently developed allosteric inhibitor asciminib with the ATP-competitive inhibitors nilotinib and dasatinib in inhibiting the BCR-Abl1 kinase activity in CML cell lines. Through these experiments, we demonstrate that asciminib significantly enhances the inhibition activity of nilotinib, but not of dasatinib. Exploring molecular mechanisms for such allosteric enhancement via systematic computational investigation incorporating molecular dynamics, metadynamics simulations, and density functional theory calculations, we found two distinct contributions. First, binding of asciminib triggers conformational changes in the inactive state of the protein, thereby making the activation process less favorable by similar to 4 kcal/mol. Second, the binding of asciminib decreases the binding free energies of nilotinib by similar to 3 and similar to 7 kcal/mol for the wildtype and T315I-mutated protein, respectively, suggesting the possibility of reducing nilotinib dosage and lowering risk of developing resistance in the treatment of CML.