Inclusion Criteria:

• Age >= 18 years
• Relapsed or refractory:
  • Groups A, B, C or D: Multiple myeloma (MM) previously treated with an immunomodulatory imide drug (IMID), a proteosome inhibitor, and an alkylating agent
  • Groups A, B, C only: Relapsed peripheral T-cell lymphoma (PTCL) of the following histologies: peripheral T-cell lymphoma-NOS (PTCL-NOS); angioimmunoblastic T-cell lymphoma (AITL), anaplastic large cell (ALCL), and mycosis fungoides (MF). Patients should have failed standard therapy and in the case of PTCL-NOS, AITL, and ALCL either have failed or be ineligible for high-dose therapy with autologous stem cell transplant
  • Group B and C only: B-cell lymphoma (other than Burkitt's lymphoma), or histiocytic/dendritic cell neoplasms (HCN) at any stage
  • Group E only: Relapsed peripheral T-cell lymphoma (PTCL) of the following histologies: peripheral T-cell lymphoma-NOS (PTCL-NOS); anaplastic large cell (ALCL), and mycosis fungoides (MF)
  • Group F only: Expansion Cohort for B-cell lymphoma (other than Burkitt's lymphoma) with low tumor burden
  • Group G only: Expansion Cohort for peripheral T cell lymphoma (PTCL) with low tumor burden
• Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =< 2 times upper limit of normal (ULN) (obtained =< 15 days prior to registration)
• Creatinine =< 2.0 mg/dL (obtained =< 15 days prior to registration)
• Direct bilirubin =< 1.5 x ULN (obtained =< 15 days prior to registration)
• International normalized ratio (INR)/prothrombin time (PT) and activated partial thromboplastin time (aPTT) =< 1.5 x ULN (obtained =< 15 days prior to registration)
• If baseline liver disease, Child Pugh score not exceeding class A (obtained =< 15 days prior to registration)
• Negative pregnancy test for persons of child-bearing potential (obtained =< 15 days prior to registration)
• FOR MULTIPLE MYELOMA ONLY: Measurable disease of multiple myeloma as defined by at least ONE of the following:
  • Serum monoclonal protein >= 1.0 g/dL by protein electrophoresis
  • >= 200 mg of monoclonal protein in the urine on 24-hour electrophoresis
  • Serum immunoglobulin free light chain >= 10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio
• FOR MULTIPLE MYELOMA ONLY: Absolute neutrophil count (ANC) >= 1000/uL (obtained =< 14 days prior to registration)
• FOR MULTIPLE MYELOMA ONLY: Platelet (PLT) >= 100,000/uL (obtained =< 14 days prior to registration)
• FOR MULTIPLE MYELOMA ONLY: Hemoglobin >= 8.5 g/dl (obtained =< 14 days prior to registration)
• FOR AML ONLY: No ANC restriction (obtained =< 14 days prior to registration)
• FOR AML ONLY: PLT >= 10,000/uL (transfusion to get platelets >= 10,000 is allowed) (obtained =< 14 days prior to registration)
• FOR AML ONLY: Hemoglobin >= 7.5 g/dl (obtained =< 14 days prior to registration)
• FOR AML ONLY: Absence of uncompensated disseminated intravascular coagulation (DIC- as diagnosed by standard International Society on Thrombosis and Hemostasis [ISTH] criteria)
• FOR TCL/BCL ONLY: ANC >= 1,000/uL (obtained =< 14 days prior to registration)
• FOR TCL/BCL ONLY: PLT >= 100,000/uL (obtained =< 14 days prior to registration)
• FOR TCL/BCL ONLY: Hemoglobin >= 8.5 g/dl (obtained =< 14 days prior to registration)
• FOR TCL/BCL ONLY: Measurable disease by CT or magnetic resonance imaging (MRI): must have at least one lesion that has a single diameter of > 2 cm or tumor cells in the blood > 5 x 10^9/L; NOTE: skin lesions can be used if the area is > 2 cm in at least one diameter and photographed with a ruler and the images are available in the medical record
• FOR HCN ONLY: ANC >= 1,000/uL obtained =< 15 days prior to registration
• FOR HCN ONLY: PLT >= 100,000/uL obtained =< 15 days prior to registration
• FOR HCN ONLY: Hemoglobin >= 8.0 g/dl obtained =< 15 days prior to registration
• FOR HCN ONLY: Measurable disease by CT or MRI: Must have at least one lesion that has a single diameter of >= 1.5 cm or tumor cells in the blood >5 x10^9/L. NOTE: Skin lesions can be used if the area is >= 1.5 cm in at least one diameter and photographed with a ruler and the images are available in the medical record
• Absence of active central nervous system (CNS) involvement; NOTE: pre-enrollment lumbar puncture not mandatory
• Ability to provide written informed consent
• Willingness to return to Mayo Clinic for follow-up
• Life expectancy >= 12 weeks
• Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2
• Willing to provide mandatory biological specimens for research purposes

Exclusion Criteria:

• Availability of and patient acceptance of curative therapy
• Uncontrolled infection
• Active tuberculosis or hepatitis, or chronic hepatitis
• Any of the following prior therapies:
  • Chemotherapy (IMIDs, alkylating agents, proteosome inhibitors) =< 2 weeks prior to registration
  • Immunotherapy (monoclonal antibodies) =< 4 weeks prior to registration
  • Experimental agent in case of AML or TCL within 4 half-lives of the last dose of the agent
• New York Heart Association classification III or IV, known symptomatic coronary artery disease, or symptoms of coronary artery disease on systems review, or known cardiac arrhythmias (atrial fibrillation or supraventricular tachycardia [SVT])
• Active CNS disorder or seizure disorder or known CNS disease or neurologic symptomatology; in case of AML active CNS involvement as detected by lumbar puncture or neuro-imaging (only to be done if clinically indicated)
• Human immunodeficiency virus (HIV) positive test result or other immunodeficiency or immunosuppression
• Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational (used for a non-Food and Drug Administration [FDA] approved indication and in the context of a research investigation);
  • NOTE: in AML, the concurrent use of hydroxyurea to help control proliferative counts is allowed throughout the treatment protocol;
  • NOTE: in TCL, patients may use topical emollients or corticosteroids, acetic acid soaks, etc. to control pruritis and prevent infection; no topical chemotherapy is allowed (no topical nitrogen mustard)
• Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown:
  • Pregnant women or women of reproductive ability who are unwilling to use effective contraception
  • Nursing women
  • Men who are unwilling to use a condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking the drug and for 4 weeks after stopping treatment
• AML ONLY: Current disseminated intravascular coagulopathy (DIC)
• ADDITIONAL EXCLUSION CRITERIA FOR GROUP A (LOW TUMOR BURDEN) ONLY:
  • Diagnosis of AML
  • Multiple myeloma only: > 25% plasma cells or plasmacytoma > 5cm in largest diameter
  • Lymphoma or HCN only: Any mass >5cm
  • Diagnosis of Burkitt's lymphoma
• ADDITIONAL EXCLUSION CRITERIA FOR GROUP B (HIGH TUMOR BURDEN) ONLY:
  • Diagnosis of AML
  • Diagnosis of Burkitt's lymphoma
• ADDITIONAL EXCLUSION CRITERIA FOR GROUP C (COMBINATION WITH CYCLOPHOSPHAMIDE) ONLY:
  • Diagnosis of AML
  • Diagnosis of Burkitt's lymphoma
• ADDITIONAL EXCLUSION CRITERIA FOR GROUP D AND E (COMBINATION WITH IPILIMUMAB AND NIVOLUMAB) ONLY:
  • Diagnosis of AML
  • Diagnosis of AITL
  • Hypersensitivity to ipilimumab or its excipients
• ADDITIONAL EXCLUSION CRITERIA FOR GROUP F (BCL EXPANSION COHORT) ONLY:
  • Diagnosis of Burkitt's lymphoma
• ADDITIONAL EXCLUSION CRITERIA FOR GROUP G (PTCL EXPANSION COHORT) ONLY:
  • Diagnosis of cutaneous TCL