This randomized phase II trial studies how well nivolumab with or without ipilimumab works in treating patients with sarcoma that has spread from the primary site to other parts of the body (metastatic) or cannot be removed by surgery (unresectable). Immunotherapy with monoclonal antibodies, such as nivolumab and ipilimumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. It is not yet known whether nivolumab works better with or without ipilimumab in treating patients with metastatic or unresectable sarcoma.

PRIMARY OBJECTIVE:

I. To evaluate the confirmed response rate of single agent nivolumab and dual agent nivolumab plus ipilimumab in patients with locally advanced/unresectable or metastatic soft tissue sarcoma.

SECONDARY OBJECTIVES:

I. To evaluate adverse event rates (National Cancer Institute [NCI] Common Terminology Criteria for Adverse Events [CTCAE] version [v]4.0) within each treatment arm.

II. To evaluate duration of response, clinical benefit rate, time to progression, progression-free survival, and overall survival within each treatment arm.

CORRELATIVE SCIENCE OBJECTIVES:

I. To potentially detect an early signal of confirmed response rate within a histologically defined patient cohort.

II. To assess the potential association between programmed cell death 1 ligand 1 (PD-L1) expression (by immunohistochemistry [IHC]) and clinical outcome, within each treatment.

III. To evaluate associations between selected biomarker measured in serial peripheral blood and with clinical efficacy, within each treatment.

IV. To evaluate the association between selected biomarker measured in tumor tissue with clinical efficacy, within each treatment.

V. To evaluate the association between baseline tumor mutational burden and neoantigen production with clinical efficacy within each treatment.

EXPLORATORY PHASE II OBJECTIVES (CROSSOVER TREATMENT):

I. To evaluate secondary endpoints within patients crossing over to dual agent nivolumab plus ipilimumab after experiencing progressive disease while receiving single agent nivolumab.

II. To evaluate correlative science objectives endpoints within patients crossing over to dual agent nivolumab plus ipilimumab after experiencing progressive disease while receiving single agent nivolumab.

OUTLINE: Patients are randomized to 1 of 2 treatment arms.

ARM I: Patients receive nivolumab intravenously (IV) over 30 minutes once every 2 weeks. Cycles repeat every 42 days for up to 108 weeks in the absence of disease progression or unacceptable toxicity. Patients who progress after 10 weeks on single agent nivolumab may elect to cross over to Arm II.

ARM II: Patients receive nivolumab IV over 30 minutes and ipilimumab IV over 90 minutes once every 3 weeks for 12 weeks. Patients then receive nivolumab IV over 30 minutes every 2 weeks. Cycles repeat every 42 days for up to 108 weeks in the absence of disease progression or unacceptable toxicity. Patients who progress by imaging during the first 12 weeks of therapy may continue treatment, at the discretion of the patient and treating investigator.

After completion of study treatment, patients are followed up at 4 weeks and then every 6 months 3 years.

Inclusion Criteria:

• PRE-REGISTRATION ELIGIBILITY CRITERIA:

• Patients must have a formalin-fixed, paraffin-embedded (FFPE) tumor block OR 1 representative hematoxylin and eosin (H&E) and 20 unstained sarcoma tissue slides available for submission to central pathology review; this review is mandatory prior to registration to confirm eligibility

• REGISTRATION ELIGIBILITY CRITERIA:

• Patients must have histologically confirmed bone or soft tissue sarcoma by central pathology review

  • Patients must have histologically confirmed liposarcoma (LPS) (only dedifferentiated and pleomorphic; well differentiated not eligible), undifferentiated pleomorphic sarcoma (UPS)/malignant fibrous histiocytoma (MFH), or gastrointestinal stromal tumor (GIST)

• Measurable disease

• Locally advanced/unresectable or metastatic disease

• >= 1 prior systemic therapy for sarcoma, including adjuvant systemic therapy

• No prior therapy with ipilimumab or nivolumab, or any agent targeting programmed cell death 1 (PD-1), PD-L1 or cytotoxic T-lymphocyte-associated protein 4 (CTLA-4)

• No treatment with biologic therapy, immunotherapy, chemotherapy, investigational agent for malignancy, or radiation =< 28 days before study registration; no treatment with nitrosourea or mitomycin =< 42 days before study registration; for GIST, tyrosine kinase inhibitor can be continued for up to 3 days prior to initiation of study treatment

• Patients should have resolution of any toxic effects of prior therapy (except alopecia) to NCI CTCAE, version 4.0, grade 1 or less

• No history of the following:

  • Active known or suspected autoimmune disease

  • Patients with human immunodeficiency virus (HIV) are eligible if the lymphocytes > 350 cluster of differentiation (CD)4+ cells and no detectable viral load

  • Symptomatic, untreated, or uncontrolled brain metastases present

  • Active autoimmune colitis

  • Autoimmune panhypopituitarism

  • Autoimmune adrenal insufficiency

  • Known active hepatitis B or C

    • Hepatitis B can be defined as:

      • Hepatitis B surface antigen (HBsAg) > 6 months
      • Serum hepatitis B virus (HBV) deoxyribonucleic acid (DNA) 20,000 IU/ml (105 copies/ml), lower values 2,000-20,000 IU/ml (104-105 copies/ml) are often seen in hepatitis B e antigen (HBeAg)-negative chronic hepatitis B
      • Persistent or intermittent elevation in alanine aminotransferase (ALT)/alanine aminotransferase (AST) levels
      • Liver biopsy showing chronic hepatitis with moderate or severe necroinflammation

    • Hepatitis C can be defined as:

      • Hepatitis C antibody (Ab) positive
      • Presence of hepatitis C virus (HCV) ribonucleic acid (RNA)

  • Known active pulmonary disease with hypoxia defined as:

    • Oxygen saturation < 85% on room air or
    • Oxygen saturation < 88% despite supplemental oxygen

• No systemic treatment with either corticosteroids (> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of registration

• Not pregnant and not nursing because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects; therefore for women of childbearing potential only, a negative pregnancy test done =< 7 days prior to registration is required

• Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1

• Absolute neutrophil count (ANC) >= 1,500/mm^3

• Platelet count >= 100,000/mm^3

• Creatinine =< 1.5 x upper limit of normal (ULN) OR calculated (calc.) creatinine clearance > 45 mL/min using the lean body mass formula only (Modified Cockcroft and Gault; Shargel and Yu 1985)

• Total bilirubin =< 1.5 x upper limit of normal (ULN) in absence of Gilbert disease (total bilirubin =< 3 x ULN with Gilbert); also, if hyperbilirubinemia is clearly attributed to liver metastases total bilirubin =< 3 x ULN is permitted

• AST/ALT =< 3 x upper limit of normal (ULN)

• Thyroid stimulating hormone (TSH) within normal limits (WNL); supplementation is acceptable to achieve a TSH WNL; in patients with abnormal TSH if free T4 is normal and patient is clinically euthyroid, patient is eligible

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): Measurable disease

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): Locally advanced/unresectable or metastatic disease

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): Patient MUST have had progressive disease (radiographic or clinical) while on arm 1 single agent nivolumab while registered to A091401

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): Patients removed from any immunotherapy for reasons other than progressive disease, including arm 1 single agent nivolumab of A091401, are NOT eligible for re-registration

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): Patients must have completed a minimum of 10 weeks of single agent nivolumab on arm 1 of A091401 to be eligible for re-registration

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): Patients must have completed study drug on arm 1 of A091401 (i.e., last dose of nivolumab) =< 12 months of re-registration to crossover dual agent therapy

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): No treatment with immunotherapy =< 21 days before re-registration; no treatment with biologic therapy, chemotherapy, investigational agent for malignancy, or radiation =< 28 days before re-registration; no treatment with nitrosourea or mitomycin =< 42 days before re-registration

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): Patients should have resolution of any toxic effects of prior therapy (except fatigue and alopecia) to NCI CTCAE, version 4.0, grade 1 or less, including immune toxicity

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): No systemic treatment with either corticosteroids (> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of re-registration

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): Not pregnant and not nursing because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects; therefore, for women of childbearing potential only, a negative pregnancy test done =< 7 days prior to re-registration is required

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): ECOG performance status 0 or 1

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): ANC >= 1,500/mm^3

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): Platelet count >= 100,000/mm^3

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): Creatinine =< 1.5 ULN OR calc. creatinine clearance > 45 mL/min (using lean body mass formula only [Modified Cockcroft and Gault; Shargel and Yu 1985])

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): Total bilirubin =< 1.5 x ULN in absence of Gilbert disease (total bilirubin =< 3 x ULN with Gilbert); if hyperbilirubinemia is clearly attributed to liver metastases, total bilirubin =< 3 x ULN is permitted

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): AST/ALT =< 3 x ULN

• RE-REGISTRATION ELIGIBILITY CRITERIA (FOR PATIENTS WHO CROSSOVER FROM ARM 1 NIVOLUMAB ALONE TO DUAL AGENT NIVOLUMAB AND IPILIMUMAB UPON PROGRESSION): TSH WNL; supplementation is acceptable to achieve a TSH WNL; in patients with abnormal TSH, if free T4 is normal and patient is clinically euthyroid, patient is eligible