BCR-ABL1 point mutation-mediated resistance to tyrosine kinase inhibitor (TKI) therapy in Philadelphia chromosome-positive (Ph⁺) leukemia is effectively managed with several approved drugs, including ponatinib for BCR-ABL1^T315I-mutant disease. However, therapy options are limited for patients with leukemic clones bearing multiple BCR-ABL1 mutations. Asciminib, an allosteric inhibitor targeting the myristoyl-binding pocket of BCR-ABL1, is active against most single mutants but ineffective against all tested compound mutants. We demonstrate that combining asciminib with ATP site TKIs enhances target inhibition and suppression of resistant outgrowth in Ph⁺ clinical isolates and cell lines. Inclusion of asciminib restores ponatinib's effectiveness against currently untreatable compound mutants at clinically achievable concentrations. Our findings support combining asciminib with ponatinib as a treatment strategy for this molecularly defined group of patients.