Inclusion Criteria:

          -  All participants must have one of the following histologically confirmed tumors at
             original diagnosis or relapse:

               -  Stratum 1

                    -  Malignant rhabdoid tumor (MRT)

                    -  Rhabdoid tumor of the kidney (RTK)

                    -  Epithelioid sarcoma

                    -  Chordoma (poorly differentiated or de-differentiated)

                    -  Other INI1-negative malignant tumors (with PI approval)

               -  Stratum 2

                    -  Atypical teratoid rhabdoid tumor (ATRT)

                    -  Other INI1-negative primary CNS malignant tumors (with PI approval)

          -  All participants must have tumor assessment at original diagnosis or relapse showing
             the following:

               -  Loss of INI1 confirmed by immunohistochemistry (IHC), OR

               -  Molecular confirmation of tumor bi-allelic SMARCB1 (INI1) loss or mutation when
                  INI1 IHC is equivocal or unavailable

          -  Relapsed or refractory disease and no standard treatment options as determined by
             locally or regionally available standards of care and treating physician's discretion

          -  Measurable disease as defined by RECIST v1.1 (Stratum 1) or RANO criteria (Stratum 2)

          -  Karnofsky performance status ≥ 50% for participants ≥16 years of age and Lansky
             performance status ≥ 50% for participants <16 years of age

          -  Participants must have fully recovered from the acute toxic effects of all prior
             anti-cancer therapy. Participants must meet the following minimum washout periods
             prior to first day of study treatment:

               -  Myelosuppressive chemotherapy: At least 14 days after the last dose of
                  myelosuppressive chemotherapy

               -  Radiotherapy

                    -  At least 14 days after local palliative XRT (small port)

                    -  At least 90 days must have elapsed after prior TBI, craniospinal XRT or if
                       >50% radiation of pelvis

                    -  At least 42 days must have elapsed if other substantial BM radiation

                    -  At least 42 days must have passed since last radionuclide therapy (e.g.
                       samarium or radium)

               -  Small molecule biologic therapy: At least 7 days following the last dose of a
                  nonmonoclonal biologic agent

               -  Monoclonal antibody: At least 21 days after the last dose

               -  Myeloid growth factors: At least 14 days following the last dose of long-acting
                  growth factor (e.g. Neulasta) or 7 days following short-acting growth factor

               -  Stem Cell or Autologous T Cell Infusion: At least 42 days must have elapsed after
                  stem cell or autologous T cell infusion

          -  Participants must have adequate organ function as defined below

               -  Bone Marrow Function

                    -  Absolute neutrophil count ≥500/uL

                    -  Hemoglobin ≥8 g/dL and transfusion independent

                    -  Platelets ≥50,000/uL and transfusion independent

               -  Hepatic Function

                    -  Total bilirubin ≤ 1.5 x upper limit of normal for age

                    -  ALT (SGPT) ≤ 3 x upper limit of normal

               -  Renal function

                    -  A serum creatinine within protocol limits based on age/sex. OR

                    -  Creatinine clearance ≥ 70 mL/min/1.73 m2 for participants with creatinine
                       levels above institutional normal

               -  Adequate Pulmonary Function Defined as: no evidence of dyspnea at rest, no
                  exercise intolerance due to pulmonary insufficient and a pulse oximetry > 92%
                  while breathing room air

               -  Adequate pancreatic function defined as serum lipase ≤ ULN at baseline

               -  Negative B-HCG pregnancy test in females of childbearing potential (must be drawn
                  within 24 hours prior to initial administration of nivolumab)

               -  Women of childbearing potential (WOCBP) receiving nivolumab agree to adhere to
                  contraception for a period of 5 months after the last dose of nivolumab. Men
                  receiving nivolumab and who are sexually active with WOCBP will agree to adhere
                  to contraception for a period of 7 months after the last dose of nivolumab.

               -  Ability to understand and/or the willingness of the patient (or parent or legally
                  authorized representative, if minor) to provide informed consent using an
                  institutionally approved informed consent procedure.

        Exclusion Criteria:

          -  Participants who are receiving any other investigational agents.

          -  Participants must not be receiving concomitant systemic steroid medications The use of
             physiologic doses of corticosteroids (up to 5 mg/m2/day prednisone equivalent) may be
             approved after consultation with the PI (treatment with topical, inhaled or ophthalmic
             corticosteroid is acceptable)

          -  Participants with a known history of HIV, hepatitis B, and/or hepatitis C

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection or any other concurrent disease which in the judgment of the Investigator
             would make the subject inappropriate for enrollment on this study

          -  Has a history of (non-infectious) pneumonitis that required steroids or has current
             pneumonitis

          -  Has active autoimmune disease that has required systemic treatment in the past 12
             months, or a documented history of clinically severe autoimmune disease, or a syndrome
             that requires systemic steroids or immunosuppressive agents. Subjects with vitiligo or
             resolved childhood asthma/atopy are exceptions. Intermittent use of bronchodilators or
             local steroid injections are not excluded. Replacement therapy (e.g. thyroxine,
             insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary
             insufficiency, etc.) is not considered a form of systemic treatment. Autoimmune
             diagnoses not listed must be approved by the Principal Investigator.

          -  Patients who have received prior solid organ transplantation are not eligible.

          -  Pregnancy or Breast-Feeding. Pregnant or breast-feeding women will not be entered on
             this study due to risks of fetal and teratogenic adverse events as there is yet no
             available information regarding human fetal or teratogenic toxicities. Pregnancy tests
             must be obtained in girls who are post-menarchal.

          -  Has received prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2 or anti-CTLA4
             agent or with an agent directed to another stimulatory or co-inhibitory T-cell
             receptor (e.g. OX-40, CD137)

          -  Participants who have received live / attenuated vaccine within 30 days of first dose
             of study treatment.