Background/Objectives: Acute myeloid leukemia (AML) is characterized by therapeutic failure and long-term risk for disease relapses. As several therapeutic targets participate in networks, they can rewire to eventually evade single-target drugs. Hence, multi-targeting approaches are considered on the expectation that interference with many different components could synergistically hinder activation of alternative pathways and demolish the network one-off, leading to complete disease remission. Methods: Herein, we established a network-based, computer-aided approach for the rational design of drug combinations and de novo agents that interact with many AML network components simultaneously. Results: A reconstructed AML network guided the selection of suitable protein hubs and corresponding multi-targeting strategies. For proteins responsive to existing drugs, a greedy algorithm identified the minimum amount of compounds targeting the maximum number of hubs. We predicted permissible combinations of amiodarone, artenimol, fostamatinib, ponatinib, procaine, and vismodegib that interfere with 3–8 hubs, and we elucidated the pharmacological mode of action of procaine on DNMT3A. For proteins that do not respond to any approved drugs, namely cyclins A1, D2, and E1, we used structure-based de novo drug design to generate a novel triple-targeting compound of the chemical formula C15H15NO5, with favorable pharmacological and drug-like properties. Conclusions: Overall, by integrating network and structural pharmacology with molecular modeling, we determined two complementary strategies with the potential to annihilate the AML network, one in the form of repurposable drug combinations and the other as a de novo synthesized triple-targeting agent. These target–drug interactions could be prioritized for preclinical and clinical testing toward precision medicine for AML.