Nivolumab With or Without Ipilimumab in Treating Younger Patients With Recurrent or Refractory Solid Tumors or Sarcomas

Inclusion Criteria

• Parts A & C: patients must be >= 12 months and = 12 months and = = 12 months and = 50% for patients > 16 years of age and Lansky >= 60 for patients = = 21 days after the completion of interleukins, interferon or cytokines (other than hematopoietic growth factors)
• Antibodies: >= 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade = = 14 days after local XRT; >= 150 days after total body irradiation (TBI), craniospinal XRT or if radiation to >= 50% of the pelvis; >= 42 days if other substantial bone marrow (BM) radiation.
• Radiopharmaceutical therapy (e.g., radiolabeled antibody, 131I-MIBG): >= 42 days must have elapsed since systemically administered radiopharmaceutical therapy
• Cellular therapy: >= 42 days must have elapsed since the completion of any type of cellular therapy (e.g. modified T cells, natural killer [NK] cells, dendritic cells, etc.)
• Patients must not have received prior exposure to nivolumab; for patients enrolled in Parts C, D, and E patients must not have received prior nivolumab or ipilimumab
• For patients with solid tumors without known bone marrow involvement:
• Peripheral absolute neutrophil count (ANC) >= 750/mm^3
• Platelet count >= 75, 000/mm^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment)
• Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts above (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; at least 5 of every cohort of 6 patients with a solid tumor must be evaluable for hematologic toxicity, for Parts A and C; if dose-limiting hematologic toxicity is observed on either Part A or C, all subsequent patients enrolled must be evaluable for hematologic toxicity on that Part
• Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70 ml/min/1.73 m^2 or a serum creatinine based on age/gender as follows:
• Age 1 to = 16 years: 1.7 for males and 1.4 for females
• Bilirubin (sum of conjugated + unconjugated) = 92% while breathing room air
• Serum lipase = = 14 days must have elapsed since last dose of corticosteroid; Note: use of topical or inhaled corticosteroids will not render a patient ineligible
• Patients who are currently receiving another investigational drug are not eligible
• Patients who are currently receiving other anti-cancer agents are not eligible
• Patients with CNS tumors or known CNS metastases will be excluded from this trial; patients with a history of CNS metastases that have been previously treated may enroll if sequential imaging shows not evidence for active disease; patients with extra axial disease (e.g. skull [bone] metastasis that do not invade the dura) may enroll if there is no evidence for CNS edema associated with the lesion
• Patients with a history of any grade autoimmune disorder are not eligible; asymptomatic laboratory abnormalities (e.g. antinuclear antibody [ANA], rheumatoid factor, altered thyroid function studies) will not render a patient ineligible in the absence of a diagnosis of an autoimmune disorder
• Patients with >= grade 2 hypothyroidism due to history of autoimmunity are not eligible; note: hypothyroidism due to previous irradiation on thyroidectomy will not impact eligibility
• Patients who have an uncontrolled infection are not eligible
• Patients with a history of congestive heart failure (CHF) or are at risk because of underlying cardiovascular disease or exposure to cardiotoxic drugs must have adequate cardiac function as clinically indicated:
• Corrected QT interval (QTC) = = 27% by echocardiogram or ejection fraction of >= 50% by gated radionuclide study
• Patients with known human immunodeficiency virus (HIV) or hepatitis B or C are excluded
• Patients who have r