Bosutinib in Treating Patients With Chronic Myeloid Leukemia in Chronic Phase After Frontline TKI Failure

Inclusion Criteria: * Patients with chronic myeloid leukemia (CML) in chronic phase who have resistance and/or intolerance to frontline TKI therapy; resistance is defined as lack (lack defined as response not achieved or lost by the given dates mentioned hereafter) of CHR (complete hematologic response) within 3 months, lack of major cytogenetic response (MCyR) within 6 months, and lack of CCyR within 12 months of therapy with frontline TKIs; in addition, loss of MCyR, CCyR or MMR at any time during the course of therapy is also considered resistance to therapy; intolerance is defined as persistent or severe toxicity that is unacceptable to the patient * Chronic phase disease is defined as: * \< 15% blasts in peripheral blood and bone marrow; * \< 30% blasts plus promyelocytes in peripheral blood and bone marrow; * \< 20% basophils in peripheral blood; * \>= 100 x 10\^9/L platelets (\>= 100,000/mm\^3); * No evidence of extramedullary disease except hepatosplenomegaly; and * No prior diagnosis of accelerated phase (AP) or blastic phase-chronic myeloid leukemia (BP-CML); patients with clonal evolution but no other criteria for accelerated phase are eligible * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 * Creatinine less than or equal to 2.0 mg/dl * Bilirubin less than or equal to 2.0 mg/dl * Alanine aminotransferase (ALT) less than or equal to 3 times institutional upper limit of normal * Females of childbearing potential must have a negative serum or urine beta human chorionic gonadotrophin (beta-hCG) pregnancy test result within 14 days prior to the first dose of study drugs and must agree to use one of the following effective contraception methods during the study and for 30 days following the last dose of study drug; effective methods of birth control include: * Birth control pills, shots or implants (placed under the skin by a health care provider) or patches (placed on the skin); * Intrauterine devices (IUDs); * Condom or occlusive cap (diaphragm or cervical/vault caps) used with spermicide; females of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy * Males who have partners of childbearing potential must agree to use an effective contraceptive method during the study and for 30 days following the last dose of study drug * Patients or their legally authorized representative must provide written informed consent Exclusion Criteria: * Women who are pregnant or lactating * Known to be human immunodeficiency virus (HIV)+ * Active and uncontrolled disease/infection that in the opinion of the treating physician and principal investigator may affect the ability to participate in the trial or put the patient at unduly high risk * Unable or unwilling to sign the informed consent document * Received no other investigational therapy within the past 14 days * Presence of T315I mutation by ABL1 sequencing * Patient is currently in complete cytogenetic remission (CCyR)