<p>Acute lymphoblastic (ALL) and chronic myeloid (CML) leukemias are blood cancers that often resist traditional chemotherapy and other treatments. This is likely due to their ability to evade apoptosis. Therefore, inducing apoptosis in leukemia cells using innovative drug combinations may be the most effective therapeutic approach. Methods for multidrug combinations involving three or more drugs are scarce and much more complex to analyze. To address this issue, we propose an effective concentration 50 (EC₅₀)-based, three-step method. The first step determines the lowest EC₅₀ for each drug (e.g., artemisinin, chloroquine, primaquine, mefloquine, ivermectin, moxidectin, doxorubicin, and minocycline) by analyzing four cell endpoints (e.g., cell cycle, sub-G1, mitochondrial membrane potential (ΔΨ_m), autophagy (lysosomes), and cleaved caspase 3 (CC3)) on K562 cells. Step two involves establishing the deleterious effect of the EC₅₀-based drug combination at concentrations of single drugs at 1-, ½-, and ¼-EC₅₀, respectively, on K562 leukemia cells. Step three involves using the optimal combined drugs to evaluate the same cellular endpoints in other non-leukemic and leukemic cells. We found that the combination of AM (1 µM), MD (10 µM), and DR (1.5 µM), i.e., at ½ EC₅₀, induced cell cycle arrest in the S (25% ± 13, <i>N</i> = 4) and G2/M (55% ± 18, <i>N</i> = 4) phases, a drastic loss of ΔΨ_m (81% ± 6, <i>N</i> = 4), high lysosome accumulation (82% ± 10, <i>N</i> = 4), and CC3 (83% ± 13, <i>N</i> = 4), as evidence of apoptosis in K562 and Jurkat cells and ex vivo ALL and CML cells. The combined drugs were innocuous to peripheral blood lymphocytes (PBLs) (S phase = 40%; G2/M = 26%; ΔΨ_m = 4%; lysosomes = 3%; CC3 = 4%; <i>n</i> = 3). Our approach to combining drugs has the potential to provide a new pharmacological treatment for leukemias.</p>