Autologous B7-H3 Chimeric Antigen Receptor T Cells in Previously Treated Extensive-Stage Small Cell Lung Cancer With Recurrent or Refractory Disease

* INCLUSION CRITERIA: * Age \>=18 years old. * Histologically confirmed small cell lung cancer (SCLC) or extrapulmonary neuroendocrine cancers (EP-NEC) that has recurred following or is refractory to first-line therapy. Note: small cell cancers of non-lung primary sites are also eligible. * Eastern Cooperative Oncology Group Performance Status (ECOG PS) 0-2. * Pulse oximetry \>= 90% on room air. * Aspartate Transferase (AST) \< 3 X institutional upper limit of normal (ULN). Note: in case of liver metastases \<= 5 X ULN is acceptable. * Alanine Aminotransferase (ALT) \< 3 X institutional ULN. Note: in case of liver metastases \<= 5 X ULN is acceptable. * Total bilirubin \<=2 X institutional ULN. * Creatinine \<=1.5 X institutional ULN OR creatinine clearance (CrCl) \>= 50 mL/min/1.73m\^2 (calculated by the Chronic Kidney Disease Epidemiology Collaboration \[CKD-EPI\] formula or calculated eGFR provided by a laboratory). * Absolute Neutrophil Count (ANC) \>= 750/mcL. * Platelet count \>= 75,000/mcL. * An absolute lymphocyte count (ALC) \>=300/mcL and CD3+ cell count \>=150/mcL. * Normal cardiac ejection fraction as defined by \>= 45% by echocardiogram (ECHO) at screening. * At least 1 measurable lesion by Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 that has not been previously irradiated. * Recovered from acute toxic effects of all prior cancer therapy to Grade \<2 per Common Terminology Criteria for Adverse Events (CTCAE) v.6.0 at least one week before apheresis excluding the parameters for ANC and ALC mentioned above. * The following criteria must be met prior to apheresis: * Chemotherapy and biologic/targeted agents: * \>=14 days since the last dose of standard myelosuppressive chemotherapy. * \>= 7 days since the completion of biologic agent, targeted agent, or tyrosine kinase inhibitor therapy. * \>= 3 weeks or 5 half-lives (whichever is shorter) since prior therapy with a monoclonal antibody. * Radiotherapy: * \>= 1 week since the last radiotherapy session. * No washout period required for palliative radiation to non-target lesions. * \>= 3 weeks since hepatic radiation, chemoembolization, and/or radiofrequency ablation. * Steroids and immunosuppressive therapy: * Corticosteroids: \>= 2 weeks since the therapeutic doses (\> 0.5 mg/kg/day prednisone or equivalent). Note: Inhaled or topical steroids are not exclusionary. * Physiologic replacement doses (up to 5 mg/day prednisone equivalent) are allowed and can be adjusted based on participant's BMI if warranted. * \>= 2 weeks since the other immunosuppressive medication (e.g., calcineurin inhibitors, methotrexate, rapamycin, thalidomide, etc.). * Anti-PD-1 and any investigational therapies: * \>= 2 weeks since Anti-PD-1 monoclonal antibody therapy. * \>= 2 weeks or 5 half-lives of the investigational product (whichever is shorter) since any investigational treatment or clinical trial participation. * Other criteria: * 72 hours since small molecule tyrosine kinase inhibitors (e.g., EGFR inhibitors), PARP inhibitors, or KRAS G12C inhibitors. * Individuals of childbearing potential (IOCBP) must agree to use highly effective contraception (hormonal, intrauterine device \[IUD\], abstinence, surgical sterilization) at the study entry and up to 12 months after the last dose of combined chemotherapy. Note: IOCBP is defined as any individual who has experienced menarche and who has not undergone successful surgical sterilization or who is not postmenopausal. * Individuals able to father a child must agree to use an effective method of contraception (barrier, surgical sterilization, abstinence) at the study entry and up to 7 months after the last dose of study drugs. We also will recommend individuals able to father a child with partners of childbearing potential ask partners to be on highly effective birth control (hormonal, IUD, surgical sterilization). Individuals able to father a child must not freeze or donate sperm within the same period. * Nursing participants must be willing to discontinue nursing from study treatment initiation through 6 months after the last dose of the study drug(s). * Ability of the participant to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: * History of anaphylactic reactions attributed to anti-B7-H3 antibodies or compounds of similar chemical or biologic composition to autologous B7-H3 CAR T cells, cyclophosphamide, fludarabine, or other agents used in this study. * Infection exposure with the human immunodeficiency virus (HIV), hepatitis B virus (HBV), or hepatitis C virus (HCV) as defined below: * Positive serology for HIV. * Active HBV infection as demonstrated by test for hepatitis B surface antigen (HBsAg). * Positive serology for HCV. * Prior gene therapy using an integrating vector (except for autologous B7-H3 CAR T cells retreatment). * History of any previous allogeneic hematopoietic stem cell transplant. * Presence of fungal, bacterial, viral, or other infection is permitted if responding to active treatment. * Central Nervous System (CNS) disorder such as cerebrovascular ischemia/hemorrhage, dementia, cerebellar disease, or autoimmune disease with CNS involvement that may impair the ability to evaluate neurotoxicity. * Pregnancy confirmed with beta-human chorionic gonadotropin (beta-HCG) serum or urine pregnancy test in IOCBP at screening. * Uncontrolled intercurrent illness or medical condition(s) evaluated by medical history, physical exam, electrocardiogram (ECG) or situations that would unacceptably increase risk for the participant or impair the ability to evaluate the endpoints of the study.