The following criteria is provided for health care professionals.

Inclusion Criteria:

• Histologically or cytologically confirmed hematologic malignancy
• The following malignancies will be considered eligible if progressive or persistent:
  • Chronic lymphocytic leukemia (CLL)
  • Non-Hodgkin lymphoma (NHL)
  • Hodgkin lymphoma (HL)
  • Multiple myeloma (MM)
  • Acute leukemia (acute myeloid leukemia [AML], acute lymphoblastic leukemia [ALL])
  • Myelodysplastic syndrome (MDS)
  • Myeloproliferative neoplasms (MPN)
  • Chronic myeloid leukemia (CML)
• Life expectancy of greater than 3 months
• Must have undergone allogeneic hematopoietic stem cell transplantation (HSCT) (regardless of stem cell source)
• Must have baseline donor T cell chimerism of >= 20%
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2
• Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (unless due to Gilbert's disease or disease-related hemolysis, then =< 3.0 x ULN)
• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 3.0 x institutional ULN
• Creatinine =< 1.5 x institutional ULN
• Prednisone dose =< 5 mg/day and off all other systemic immunosuppressive medications for at least 4 weeks prior to study entry
• Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

• Participants who have had anti-tumor therapy or other investigational agents within 4 weeks prior to registration (6 weeks for nitrosoureas or mitomycin C), or those who have not recovered from adverse events due to agents administered more than 4 weeks prior to registration
• Patients with prior history of severe (grade 3 or 4) acute graft-versus-host disease (GVHD)
• Patients with a history of prior treatment with ipilimumab, anti-programmed cell death protein 1 (PD 1) antibody, or cluster of differentiation (CD) 137 agonist therapy
• Patients who have had donor lymphocyte infusion (DLI) within 8 weeks prior to registration
• AUTOIMMUNE DISEASE: Patients with a history of inflammatory bowel disease, including ulcerative colitis and Crohn's disease, are excluded from this study, as are patients with a history of symptomatic disease (e.g., rheumatoid arthritis, systemic progressive sclerosis [scleroderma], systemic lupus erythematosus, autoimmune vasculitis [e.g., Wegener's granulomatosis]) and motor neuropathy considered of autoimmune origin (e.g. Guillain-Barre syndrome and myasthenia gravis); patients with Hashimoto's thyroiditis are eligible to go on study
• Patients with known chronic human immunodeficiency virus (HIV), hepatitis B or hepatitis C infections should be excluded
• Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• Pregnant women are excluded from this study