Selective Antigen Specific T Cells and CAR T Cells in Subjects With Relapsed/Refractory Embryonal Tumors (SABRE)

Inclusion Criteria: Recipient Inclusion Criteria for Procurement: * Diagnosis of relapsed/refractory rhabdomyosarcoma, Ewing sarcoma, neuroblastoma, or Wilms tumor * Refractory disease, residual detectable disease or relapsed disease following available standard of care therapies with known clinical benefit for their specific tumor type, or unable to receive such therapies due to unacceptable toxicity or contraindication * Measurable or evaluable disease by imaging, as determined following most recent therapy * Age ≥ 1 year and \< 24 years * Weight \> 10 kg * No systemic steroid exposure within 1 week of procurement * Karnofsky/Lansky score of ≥ 60 (See Appendix 3) * Participants of childbearing potential or capable of fathering a child must agree to use effective contraceptive measure/s (as described in Appendix 5) during study protocol participation through 6 months following the administration of the CAR-TA T cells * ANC \> 500/µL * ALC \> 1000/µL * Platelet count \> 50,000/uL (level can be achieved with transfusion) * Bilirubin ≤ 2.5 mg/dL * Aspartate aminotransferase (AST)/Alanine transaminase (ALT) ≤ 5x the upper limit of normal for age * Serum creatinine Maximum serum creatinine (mg/dL) Age Male Female 1. to \< 2 years 0.6 0.6 2. to \< 6 years 0.8 0.8 6 to \< 10 years 1 1 10 to \< 13 years 1.2 1.2 13 to \< 16 years 1.5 1.2 ≥ 16 years 1.7 1.4 OR Creatinine clearance or glomerular filtration rate (GFR) ≥ 70 mL/min/1.73 m for patients with levels above * For FOCBP: Negative pregnancy test * Pulse oximetry of \> 90% on room air * Adequate cardiac function defined as: o Shortening fraction of ≥ 27% by echocardiogram, or o Ejection fraction of \> 50% by echocardiogram or radionuclide angiogram (i.e., MUGA). * No acute neurological toxicity \> grade 1 (with the exception of peripheral sensory neuropathy or controlled seizure disorder on anti-epileptics). * The following time frames must have elapsed between prior therapy completion and apheresis cell collection: * Myelosuppressive chemotherapy/immunomodulatory medications: At least 3 weeks, or 6 weeks if prior nitrosourea. * Hematopoietic growth factors: At least 7 days since the completion of therapy with a growth factor. At least 14 days after receiving pegfilgrastim. * Biological agent, tyrosine kinase inhibitor, targeted agent, metronomic chemotherapy: At least 7 days since the completion of therapy with a biologic agent, tyrosine kinase inhibitor, targeted agent, or metronomic non-myelosuppressive regimen. * Monoclonal antibodies and checkpoint inhibitors: At least 3 weeks or 5 half-lives (whichever is shorter) since the last dose of a monoclonal antibody or checkpoint inhibitor. * Radiotherapy (XRT): At least 3 weeks since XRT, and at least 6 weeks if radiation involved the CNS or lung fields. Exception: There is no time restriction for palliative radiation with minimal bone marrow involvement and the patient has measurable/evaluable disease outside the radiation port or the site of radiation has documented progression. * Autologous stem cell transplant/infusion: At least 6 weeks from their infusion after an autologous stem cell infusion following myeloablative therapy. Patients who received an autologous stem cell infusion following non-myeloablative therapy do not have a wash-out period; they are eligible once they meet all other eligibility requirements, including recovery from acute side effects. * Investigational agent: at least 28 days since receiving an investigational agent. * Patient or parent/guardian capable of providing informed consent. Recipient Inclusion Criteria for CAR-TA T cell product Infusion: * No systemic steroid exposure within 1 week prior to protocol therapy initiation * Karnofsky/Lansky score of ≥ 60 (See Appendix 3) * ANC \> 750/uL * Platelet count \> 75,000/uL * Bilirubin ≤ 2.5 mg/dL * AST/ALT ≤ 5x the upper limit of normal for age * Serum creatinine Maximum serum creatinine (mg/dL) Age Male Female 1 to \< 2 years 0.6 0.6 2 to \< 6 years 0.8 0.8 6 to \< 10 years 1 1 10 to \< 13 years 1.2 1.2 13 to \< 16 years 1.5 1.2 ≥ 16 years 1.7 1.4 OR Creatinine clearance or glomerular filtration rate (GFR) ≥ 70 mL/min/1.73 m for patients with levels above * For FOCBP: Negative pregnancy test * Participants of childbearing potential or capable of fathering a child must agree to use effective contraceptive measure/s (as described in Appendix 5) through 6 months following the administration of the CAR-TA T cells * Adequate respiratory function defined as oxygen saturation 90% or higher on room air * No acute neurological toxicity \> grade 1 (with the exception of peripheral sensory neuropathy or controlled seizure disorder on anti-epileptics). * Adequate cardiac function defined as: * Shortening fraction of ≥ 27% by echocardiogram, or * Ejection fraction of \> 50% by echocardiogram or radionuclide angiogram * The following time frames must have elapsed between completion of prior therapy and the initiation of SABRE protocol therapy: * Myelosuppressive chemotherapy: At least 2 weeks from last dose of chemotherapy. * Hematopoietic growth factors: At least 7 days since the completion of therapy with a growth factor. At least 14 days after receiving pegfilgrastim. * Biological agent, tyrosine kinase inhibitor, targeted agent, metronomic chemotherapy: At least 7 days since the completion of therapy with a biologic agent, tyrosine kinase inhibitor, targeted agent, or metronomic non-myelosuppressive regimen. * Monoclonal antibodies and checkpoint inhibitors: At least 3 weeks or 5 half-lives (whichever is shorter) since the last dose of a monoclonal antibody or checkpoint inhibitor. * Radiotherapy (XRT): At least 3 weeks since XRT, and at least 6 weeks if radiation involved CNS or lung fields. Exception: There is no time restriction for palliative radiation with minimal bone marrow involvement and the patient has measurable/evaluable disease outside the radiation port or the site of radiation has documented progression. * Investigational agent: At least 28 days since receiving an investigational agent. * Patient or parent/guardian capable of providing informed consent. Exclusion Criteria: Recipient Procurement Exclusion Criteria: * Patients with known CNS disease. * Patients with uncontrolled infection/s or known HIV infection * Pregnant or lactating females. * Patients who have undergone previous allogeneic stem cell transplant. Recipient Exclusion Criteria for CAR-TA T cell product Infusions: * Patients with uncontrolled infections or known HIV infection. * Pregnant or lactating females * Whole lung/mediastinal radiation within 12 weeks * Clinically significant systemic illness or medical condition likely to interfere with assessment of safety or efficacy