As many as 65% of individuals with chronic myeloid leukemia (CML) who receive imatinib therapy do not attain a sustained deep molecular response, a critical requirement for attempting treatment-free remission. Asciminib represents the sole approved BCR::ABL1 inhibitor that selectively binds to the ABL myristoyl pocket. This novel mode of action facilitates its use in combination with ATP-competitive tyrosine kinase inhibitors, thereby helping to overcome resistance mechanisms and augment therapeutic effectiveness. The phase II ASC4MORE trial examined the addition of asciminib to imatinib in patients who had not reached deep molecular response while on imatinib. The ASC4MORE study enrolled 84 patients with CML in the chronic phase who had failed to achieve a deep molecular response after at least 1 year of imatinib treatment. Participants were randomized to one of four arms: asciminib 40 mg or 60 mg once daily (QD) added to imatinib 400 mg QD, continuation of imatinib 400 mg QD alone, or a switch to nilotinib 300 mg twice daily. At week 48 (the primary endpoint), achievement of MR4.5 (BCR::ABL1 ≤ 0.0032% on the International Scale) was substantially more frequent in the asciminib 40-mg QD add-on group (19.0%) and the 60-mg QD add-on group (28.6%) than in the continued imatinib arm (0.0%) or the nilotinib switch arm (4.8%). Treatment discontinuation occurred less often with asciminib add-on at 40 mg (14.3%) and 60 mg (23.8%) compared with continued imatinib (76.2%, including patients who crossed over) and nilotinib (47.6%). The asciminib add-on approach demonstrated acceptable tolerability, with lower rates of adverse events and treatment discontinuations due to adverse events than with nilotinib. However, rates remained higher than with continued imatinib (as would be anticipated in patients already stable on imatinib for at least 1 year). The safety profile of asciminib when added to imatinib did not reveal any novel or intensified signals beyond those previously documented with asciminib monotherapy. In summary, these outcomes indicate that adding asciminib to imatinib offers a viable strategy for helping patients with CML in chronic phase continue treatment and achieve rapid, profound molecular responses safely. However, further research is warranted before routine adoption of this approach in clinical settings.