Genetically Engineered Cells (FH-FOLR1 ST CAR T Cells) for the Treatment of Advanced Refractory or Recurrent/Progressive Osteosarcoma, FIERCe Trial

Inclusion Criteria: * Age 1-75 years at the time of enrollment * Tissue confirmation of osteosarcoma diagnosis * Must have received an anthracycline-based regimen or been deemed ineligible to receive this therapy * Must have at least one of the following in the 6 months prior to trial consent: * New site of measurable disease by radiographic imaging or histologic confirmation * New site of evaluable disease by radiographic imaging or histologic confirmation * Greater than 20% increase in at least one tumor dimension documented by CT/MRI, AND a minimum absolute increase of 5 mm in longest dimension of existing lesion(s) (previously irradiated lesions may be included) * Persistent measurable disease or fludeoxyglucose F-18 (FDG)-PET avid bone metastasis that has failed to achieve complete remission to upfront conventional therapy (surgery, radiotherapy, and/or chemotherapy) * All anti-cancer therapy must be discontinued at enrollment/time of apheresis, with the following washout periods observed: * Chemotherapy and biologic agents: ≥ 7 days prior to enrollment * Steroid use: All corticosteroid therapy (unless physiologic replacement dosing and/or topical administration (e.g., inhaled or dermatologic) ≥ 7 days prior to enrollment * Tyrosine kinase inhibitor (TKI) use: ≥ 7 days prior to enrollment * Antitumor antibody therapy (including immune checkpoint inhibitor) must be ≥ 3 half-lives or 30 days, whichever is shorter, from time of enrollment * FOLR1 targeting therapy must be discontinued at least 30 days prior to enrollment * Gene modified cellular therapy: At enrollment, must be at least 30 days from most recent gene modified cell therapy infusion and document no evidence of modified cells in the peripheral blood OR must be at least 60 days from most recent gene modified cell therapy * Washout periods not applicable to patients with apheresis product or usable T cell product available for use at time of enrollment * Potential trial participants should have recovered to grade 1 from clinically significant adverse events of their most recent therapy/intervention prior to enrollment * Ability to understand and willingness to sign a written informed consent document. * Females of child-bearing potential and fertile male participants must be willing to use an effective contraceptive method before, during, and for at least 12 months after the FOLR1 CART cell infusion * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 (if treated at adult facility) or Lansky/Karnofsky score ≥ 60 (if treated at pediatric facility). Participants who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for purposes of assessing performance status * Life expectancy ≥ 8 weeks * Able to tolerate apheresis, including placement of temporary apheresis catheter, if necessary, or already has an apheresis product available for use in manufacturing * Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Participants with treated brain metastases are eligible if they meet the following criteria: * Follow-up brain imaging taken at screening demonstrates no evidence of progression and that imaging occurs 3 months after central nervous system (CNS)-directed therapy has been completed * No ongoing, symptomatic CNS pathology requiring medical intervention * Serum creatinine ≤ 1.5 x upper limit of normal (ULN) based on age and gender; or estimated creatinine clearance \> 50 mL/min as calculated using the Cockcroft-Gault formula and not dialysis dependent * Age: 1 to \< 2 years; maximum serum creatinine (mg/dL): 0.6 (male), 0.6 (female) * Age: 2 to \< 6 years; maximum serum creatinine (mg/dL): 0.8 (male), 0.8 (female) * Age: 6 to \< 10 years; maximum serum creatinine (mg/dL): 1 (male), 1 (female) * Age: 10 to \< 13 years; maximum serum creatinine (mg/dL): 1.2 (male), 1.2 (female) * Age: 13 to \< 16 years; maximum serum creatinine (mg/dL): 1.5 (male), 1.4 (female) * Age: ≥ 16 years; maximum serum creatinine (mg/dL): 1.7 (male), 1.4 (female) * Total bilirubin ≤ 3 x ULN or conjugated bilirubin ≤ 2 mg/dL. Participants with suspected Gilbert syndrome may be included if total bilirubin (Bili) \> 3 mg/dL but no other evidence of hepatic dysfunction * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 5 x ULN * Pulmonary: ≤ grade 1 dyspnea at rest and arterial oxygen saturation (SaO2) ≥ 92% on ambient air. If pulmonary function tests (PFTs) are performed based on the clinical judgement of the treating physician, participants with forced expiratory volume in 1 second (FEVI) ≥ 50% of predicted and diffusion capacity of the lung for carbon monoxide (DLCO) (corrected) of ≥ 40% of predicted will be eligible * Left ventricular ejection fraction (LVEF) may be established with echocardiogram or MUGA scan, and left ejection fraction must be ≥ 50% or shortening fraction ≥ 28% * Absolute neutrophil count (ANC) ≥ 500 cells/ mm\^3 * Hemoglobin ≥ 8 g/dL * Platelets ≥ 100,000 per mm\^3 * Participants receiving blood product transfusion are acceptable as long as they are not determined to be transfusion refractory Exclusion Criteria: * Active autoimmune disease: Participants with active autoimmune disease requiring immunosuppressive therapy are excluded. Case by case exemptions are possible with approval by PI * Corticosteroid therapy at a dose equivalent of \> 15 mg of prednisone per day (or equivalent). Pulsed corticosteroid use for disease control is acceptable. For participants weighing ≤ 30 kg, systemic steroids ≥ 0.5 mg prednisone equivalent/kg/day * Concurrent use of other investigational anti-cancer agents * Active uncontrolled infection: HIV positive participants on highly active antiretroviral therapy (HAART) with a CD4 count \> 500 cells/mm\^3 are considered controlled, as are individuals with a history of hepatitis C who have successfully completed antiviral therapy with an undetectable viral load, and those with hepatitis B who have hepatitis well controlled on medication * Uncontrolled concurrent illness: Participants may not have uncontrolled or concurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, or cardiac arrhythmia that would limit compliance with study requirements * Active treatment for prior immune related adverse event to any immunotherapy: Participants receiving ongoing treatment for prior serious immune-related adverse events are excluded, with exception of hormone supplementation or corticosteroid therapy at equivalent of \> 15 mg prednisone (or equivalent) per day, unless otherwise approved by PI * Significant underlying neurologic disease: Study participants must not have significant active underlying neurologic disease, unless approved by PI. Peripheral neuropathy related to diabetes or prior chemotherapy is acceptable * Pregnant, possibly pregnant or those expecting to conceive or father children for the duration of the trial through 4 months after T cell infusion * Participants unwilling to provide consent/assent for participation in the study and 15-year follow-up period if CAR T cell therapy is administered * Other medical, social, or psychiatric factor that interferes with medical appropriateness and/or ability to comply with study, as determined by the PI * Known allergic reactions to any of the components of study treatments