Pembrolizumab and Dasatinib, Imatinib Mesylate, or Nilotinib in Treating Patients With Chronic Myeloid Leukemia and Persistently Detectable Minimal Residual Disease

Inclusion Criteria: * PREREGISTRATION (STEP 0): Patient has pathologically-confirmed chronic phase-CML on a first line TKI and must meet the following criteria: * The patient has to be on first-line TKI therapy (the same TKI) for at least 2 years prior to pre-registration * Has been in MMR (i.e. MR\^3) but still have detectable BCR-ABL transcript by a standard real-time quantitative polymerase chain reaction (RQ-PCR) assay with a limit of detection (sensitivity) of 4.5 for at least 12 months from the first documentation of the MMR * Patient has not achieved MR\^4.5 (complete molecular remission \[CMR\]) within the time of initiation of TKI therapy and pre-registration * PREREGISTRATION (STEP 0): Patient must be scheduled to undergo a standard of care bone marrow biopsy within 7 days of step 0 registration * PREREGISTRATION (STEP 0): Peripheral blood must be collected for submission to Fred Hutchinson Cancer Research Center for central assessment of the establishment of BCR/ABL status to confirm patient?s eligibility for registration to Step 1; Fred Hutchinson will forward results within 1-2 business days of receipt of the peripheral blood to the submitting institution * REGISTRATION TO TREATMENT (STEP 1): Institution has received central BCR-ABL test results confirming MRD positive status * REGISTRATION TO TREATMENT (STEP 1): Patients have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * REGISTRATION TO TREATMENT (STEP 1): No active hemolytic a…