The purpose of this study is to determine the side effects of treatment with the monoclonal antibody anti-PD-L1 (BMS-936559) in subjects with compromised bone marrow function and the dose that should be recommended for use in future studies.

Inclusion Criteria:

• Eastern Cooperative Oncology Group (ECOG) Performance of 0 or 1

• Subjects must have histological confirmation of relapsed or refractory hematologic malignancy

• Subjects with non-Hodgkin's lymphoma or Hodgkin lymphoma must have at least one measureable lesion as defined by lymphoma response criteria. Tumor sites that are considered measureable must not have received prior radiation therapy

• Subjects with multiple myeloma (MM) must have detectable disease as measured by presence of monoclonal immunoglobulin protein in a serum electrophoresis: IgG, IgA, IgM, (M-protein ≥ 0.5 g/dl or serum IgD M-protein ≥ 0.05 g/dl) or serum free-light chain or 24 hour urine with free light chain. Excluded are subjects with only plasmacytomas, plasma cell leukemia, or non-secretory myeloma

• Subjects with chronic myelogenous leukemia (CML) must have evidence of the Philadelphia chromosome by polymerase chain reaction (PCR) or chromosome analysis

• Life expectancy of at least 3 months

• For subjects with lymphoma, either a formalin fixed tissue block or 7 to 15 slides of tumor sample (archival or fresh) must be available for performance of correlative studies

• Subjects must have received at least one prior chemotherapy regimen. Subjects must be off therapy for at least 4 weeks ( 2 weeks for oral agents) prior to Day 1

• Prior palliative radiation must have been completed at least 2 weeks prior to study Day 1

• Toxicities related to prior therapy must have returned to Grade 1 or less, except for alopecia. Peripheral neuropathy must be Grade 2 or less

• Adequate bone marrow function defined as:

  1. Absolute neutrophil count ≥ 1000/μl (stable off any growth factor within 1 week of study drug administration)
  2. Hemoglobin ≥ 9 g/dL (transfusion to achieve this level is permitted)
  3. Platelet count ≥ 50 X 103/ μl (transfusion to achieve this level is not permitted)

• Adequate renal parameters defined as Creatinine clearance (CrCl) > 40 ml/min (Cockcroft-Gault formula)

• Adequate hepatic parameters defined as:

  1. Aspartate aminotransferase (AST) ≤ 3 x ULN
  2. Alanine aminotransferase (ALT) ≤ 3 x ULN
  3. Bilirubin ≤ 1.5 x ULN (except subjects with Gilbert's Syndrome, who must have total bilirubin < 3.0 mg/dL and direct bilirubin < 0.5 mg/dL)

• Women of child bearing potential (WOCBP) and for at least 70 days after the last dose of investigational product

• Men and women ≥ 18 years of age

Exclusion Criteria:

• Subjects with acute leukemias, blast phase CML, T cell lymphoblastic or Burkitt lymphoma
• Subjects with a history of central nervous system involvement by hematologic malignancy or symptoms suggestive of central nervous system involvement
• Subjects with concomitant second malignancies (except adequately treated nonmelanomatous skin cancers, ductal carcinoma in situ, treated superficial bladder cancer or prostate cancer or in situ cervical cancers) are excluded unless a complete remission was achieved at least 3 years prior to study entry and no additional therapy is required or anticipated to be required during the study period
• Subjects with any active autoimmune disease or a history of known or suspected autoimmune disease, or history of syndrome that requires systemic corticosteroids or immunosuppressive medications, except for subjects with vitiligo or resolved childhood asthma/atopy
• A serious uncontrolled medical disorder or active infection which would impair the ability of the subject to receive protocol therapy or whose control may be jeopardized by the complications of this therapy
• Prior therapy with an anti programmed death-1 (anti-PD-1), anti Programmed death ligand 1 (anti-PD-L1), anti Programmed death ligand 2 (anti-PD-L2), anti-CD137 or anti Cytotoxic T lymphocyte-associated antigen 4 (anti-CTLA-4) antibody (or any other antibody or drug specifically targeting T-cell costimulation or checkpoint pathways)
• Non-oncology vaccine therapies for prevention of infectious diseases (eg seasonal flu vaccine, Human Papilloma Virus (HPV) vaccine) within 4 weeks of study drug administration Vaccination while on study is also prohibited except for administration of the inactivated influenza vaccine
• Prior organ allograft or allogeneic bone marrow transplantation
• Positive for human immunodeficiency virus (HIV 1/2) or known acquired immunodeficiency syndrome (AIDS)
• Positive tests for hepatitis B virus surface antigen (HBsAg), or antibody to hepatitis B core Ag or hepatitis C virus antibody (confirmed by Western Blot) or hepatitis C ribonucleic acid (RNA) in serum
• Ejection fraction less than 45% in subjects with prior anthracycline exposure
• History of Grade 4 anaphylactic reaction to monoclonal antibody therapy
• Women who are pregnant or breastfeeding