HER2 Chimeric Antigen Receptor (CAR) T Cells in Combination With Checkpoint Blockade in Patients With Advanced Sarcoma

Procurement Inclusion Criteria: * Diagnosis of a HER2-positive sarcoma. Immunohistochemistry (IHC) will be used to determine HER2 expression. Standard HER2 positive breast cancer density gradient tissue microarrays will be used as positive controls. HER2 expression will be graded for percent positive tumor cells (Grade 0: no staining; Grade 1: 1-25%; Grade 2: 26-50% and Grade 3: 51-100%) and intensity of staining (Negative; 1+; 2+; and 3+). For the patient to meet eligibility, tumors are required to have at least ≥ grade 1 and ≥ 1+ intensity score for HER2 staining. * Age between 1 to 25 years * Karnofsky or Lansky performance score of ≥ 60 * Informed consent explained to, understood by, and signed by patient/guardian. Patient or guardian given copy of informed consent. Treatment Inclusion Criteria: * Diagnosis of a HER2 positive sarcoma with active disease progression or recurrence after at least one prior systemic therapy * At least 4 weeks from and having recovered from acute toxic effects of all prior cytotoxic chemotherapy. Those receiving targeted (non-cytotoxic) drugs must be at least 7 days or 3 drug half-lives, whichever is greater, from last receipt of said drug and must have recovered from all acute toxic effects of that drug. * Normal cardiac left ventricular end diastolic function (LVEF) as measured by echocardiogram (normal per institutional limits) * Karnofsky or Lansky performance score of ≥60 * Total bilirubin ≤1.5x upper limit of normal (ULN) for age AND direct bilirubin ≤ULN for age * AST/ALT ≤ 2.5x ULN * Serum creatinine ≤1.5x ULN for age * Hgb ≥ 7.0 g/dL (transfusion allowed) * WBC \> 2,000/µl * ANC \>1,000/ul * Platelets \>75,000/ul (not transfused) * Pulse oximetry of ≥ 90% on room air * Sexually active males and females of childbearing potential must agree to use a form of contraception considered effective and medically acceptable by the investigator. Non-childbearing potential is defined as pre-menarche, greater than 1-year post-menopausal, or surgically sterilized. * Available autologous transduced cytotoxic T lymphocytes with ≥ 15% expression of HER2 CAR and killing of HER2-positive targets ≥ 20% in cytotoxicity assay * Informed consent explained to, understood by, and signed by patient or guardian. Patient or guardian given copy of informed consent. Procurement Exclusion Criteria: * Known HIV positivity * Severe previous toxicity from cyclophosphamide including, but not limited to, decreased heart function, abnormal heart rhythms, severe allergic reaction, or grade 4 hemorrhagic cystitis * Severe previous toxicity from fludarabine including, but not limited to, neurotoxicity, coma, renal injury requiring dialysis, development of hemolytic anemia, or development of a secondary malignancy * Severe hypersensitivity (≥Grade 3) to pembrolizumab or nivolumab or any of their excipients * History of allergic reactions attributed to murine protein containing products, DMSO or dextran 40 * Known, active cardiac disorder defined as left ventricular ejection fraction below the institution normal as determined by echocardiogram or New York Heart Association (NYHA) functional class III or IV or clinically significant cardiac arrhythmia. Note: A new echocardiogram or EKG is not required to make this determination. * Active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs). 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 * History of non-infectious pneumonitis that required steroids or current pneumonitis * Known history of active tuberculosis * Has undergone solid organ transplantation at any time * Has a diagnosis of immunodeficiency or is receiving any other form of immunosuppressive therapy aside from cytotoxic chemotherapy * Presence of bulky tumor at the primary or metastatic site * Has a history or current evidence of any condition, therapy, or laboratory or radiologic abnormality that is not in the best interest of the subject to participate, as determined by the treating investigator Treatment Exclusion Criteria: * Known HIV positivity * Intercurrent infection * Pregnant or lactating * History of hypersensitivity to murine protein-containing products, DMSO or dextran 40 * Severe previous toxicity from cyclophosphamide including, but not limited to, decreased heart function, abnormal heart rhythms, severe allergic reaction, or grade 4 hemorrhagic cystitis * Severe previous toxicity from fludarabine including, but not limited to, neurotoxicity, coma, renal injury requiring dialysis, development of hemolytic anemia, or development of a secondary malignancy * Severe hypersensitivity (≥Grade 3) to pembrolizumab or nivolumab or any of their excipients * Cardiac disorder defined as left ventricular ejection fraction below the institution normal as determined by echocardiogram or New York Heart Association (NYHA) functional class III or IV or clinically significant cardiac arrhythmia * Active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs). 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. * History of non-infectious pneumonitis that required steroids or current pneumonitis * Known history of active tuberculosis * Has received a live virus vaccine within previous 30 days * Has undergone solid organ transplantation at any time * Has a diagnosis of immunodeficiency or is receiving any other form of immunosuppressive therapy * Presence of bulky tumor at the primary or metastatic site * Has received radiotherapy within 14 days of start of trial treatment with the exception that those who have received palliative radiation (≤ 10 days of radiotherapy) to non-central nervous system disease within 7 days are permitted. Subjects must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. * Has a history or current evidence of any condition, therapy, or laboratory or radiologic abnormality that is not in the best interest of the subject to participate, as determined by the treating investigator