Chronic myeloid leukemia is a hematological cancer driven by the oncoprotein BCR-ABL1, and lifelong treatment with tyrosine kinase inhibitors extends patient survival to nearly the life expectancy of the general population. Despite advances in the development of more potent tyrosine kinase inhibitors to induce a durable deep molecular response, more than half of patients relapse upon treatment discontinuation. This clinical finding supports the paradigm that leukemia stem cells feed the neoplasm, resist tyrosine kinase inhibition, and reactivate upon drug withdrawal depending on the fitness of the patient's immune surveillance. This concept lends support to the idea that treatment-free remission is not achieved solely with tyrosine kinase inhibitors and that new molecular targets independent of BCR-ABL1 signaling are needed in order to develop adjuvant therapy to more efficiently eradicate the leukemia stem cell population responsible for chemoresistance and relapse. Future efforts must focus on the identification of new targets to support the discovery of potent and safe small molecules able to specifically eradicate the leukemic stem cell population. In this review, we briefly discuss molecular maintenance in leukemia stem cells in chronic myeloid leukemia and provide a more in-depth discussion of the dual-specificity kinase DYRK2, which has been identified as a novel actionable checkpoint in a critical leukemic network. DYRK2 controls the activation of p53 and proteasomal degradation of c-MYC, leading to impaired survival and self-renewal of leukemia stem cells; thus, pharmacological activation of DYRK2 as an adjuvant to standard therapy has the potential to induce treatment-free remission.