Inclusion Criteria:

          -  Relapsed or refractory B-cell ALL or CML in lymphoid blast phase; Philadelphia
             chromosome must be present at screening (as determined by cytogenetic analysis,
             fluorescence in situ hybridization [FISH], or polymerase chain reaction [PCR] [i.e.,
             BCR-ABL positive]); Note: patients with CML who have received treatment with tyrosine
             kinase inhibitors for their CML, and have progressed to lymphoid blast phase are
             eligible for frontline treatment; Frontline Ph+ ALL or CML-lymphoid blast phase (LBC)
             Cohort: Patients with newly-diagnosed Ph+ ALL or CML-LBC, who have received no or
             minimal treatment (minimal treatment is defined as treatment with steroids/hydroxyurea
             of =< 2 week duration; vincristine =< 2 doses; tyrosine kinase inhibitor of =< 4 week
             duration; =< 2 doses of cytarabine) and are >= 60 years or older are eligible;
             patients must have bone marrow blasts > 5% at the time of screening

          -  Expression of CD-22 in >= 20% blasts

          -  Eastern Cooperative Oncology Group (ECOG) performance status score of < or = 2

          -  Serum bilirubin < or = 2.0 mg/dl

          -  Serum creatinine < or = 2.0 mg/dl

          -  Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) < or = 3 x upper
             limit of normal (ULN)

          -  Females of childbearing potential must have a negative serum or urine beta human
             chorionic gonadotropin (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,
             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:

          -  History of another primary invasive malignancy that has not been definitively treated
             or in remission for at least 2 years; patients with non-melanoma skin cancers or with
             carcinomas in situ are eligible regardless of the time from diagnosis (including
             concomitant diagnoses)

          -  Patients with active unstable angina, concomitant clinically significant active
             arrhythmias, myocardial infarction within 6 months, or congestive heart failure New
             York Heart Association class III-IV; patients with a cardiac ejection fraction (as
             measured by either multi gated acquisition scan [MUGA] or echocardiogram) < 40% are
             excluded

          -  Known evidence of active cerebral/meningeal disease; patients may have history of
             central nervous system (CNS) leukemic involvement if definitively treated with prior
             therapy and no evidence of active disease (defined as >= 2 consecutive spinal fluid
             assessments with no evidence of disease) at that time of registration

          -  Previous treatment with any anti-CD22 directed therapy

          -  Patients with previous allogeneic stem cell transplant (SCT) if they meet either of
             the following criteria:

               -  < 100 days from allogeneic SCT

               -  Active acute or chronic graft-versus-host disease (GvHD), or

               -  Receiving immunosuppressive therapy as treatment for GvHD within the last 7 days

          -  Patients with uncontrolled active infections (viral, bacterial, or fungal) are not
             eligible

          -  Active hepatitis B or C infection, or known seropositivity for human immunodeficiency
             virus (HIV)

          -  Patients with liver cirrhosis or other serious active liver disease or with suspected
             alcohol abuse

          -  History of autoimmune diseases (such as systemic lupus erythematosus [SLE], Wegener's,
             Wegener's granulomatosis, polyarteritis nodosa); Note: Prior autoimmune diseases are
             allowed as long as clinically stable

          -  Prior chemotherapy/radiotherapy/investigational therapy within 2 weeks before the
             start of study drugs with the following exceptions:

               -  To reduce the circulating lymphoblast count or palliation: steroids, hydroxyurea;
                  no washout necessary for these agents

               -  For ALL maintenance/CML treatment: mercaptopurine, methotrexate, vincristine,
                  single-agent, single-dose of cytarabine and/or tyrosine kinase inhibitors; these
                  agents should be discontinued at least 48 hours prior to start of study drugs;
                  (Note: the interval of time from last dose of any approved tyrosine kinase
                  inhibitor [TKI] to start of protocol treatment is 48 hours regardless of the
                  indication for treatment with the TKI)

          -  Patients who have not recovered from acute non hematologic toxicity (to =< grade 1) of
             all previous therapy prior to enrollment

          -  Females who are pregnant or lactating

          -  Other severe acute or chronic medical or psychiatric condition or laboratory
             abnormality that in the opinion of the investigator may increase the risk associated
             with study participation or investigational product administration or may interfere
             with the interpretation of study results and/or would make the patient inappropriate
             for enrollment into this study

          -  Patients previously exposed to bosutinib are eligible unless they carry T315I

          -  Patients with T315I mutations will be excluded (this criteria is not applicable for
             the frontline Ph+ ALL or CML-LBC cohort)