GPC3 Targeted CAR-T Cell Therapy in Advanced GPC3 Expressing Hepatocellular Carcinoma (HCC)

Inclusion Criteria

• - INCLUSION CRITERIA: - Histopathological confirmation of HCC by the NCI Laboratory of Pathology - Participants must: - have progressed on the prior first line of standard therapy OR --been intolerant of the standard of care chemotherapy for HCC. - Participants must have at least 1 focus of disease that is amenable to mandatory tumor biopsy prior to study treatment initiation to determine tumor GPC3 expression and be willing to undergo this. Ideally, the biopsied lesion should not be one of the target measurable lesions, although this can be up to the discretion of the investigators. - Tumor must have GPC3 positivity of >= 25% by immunohistochemistry on freshly collected biopsy - Participants must have at least 1 measurable lesion by RECIST version 1.1 - Participants must have a disease that is not amenable to potentially curative resection, ablation, or transplantation. - Age >= 18 years. - Performance status (ECOG) 0-1 - Participants must have adequate organ and marrow function as defined below: ANC: >= 1,000/mcL Platelets: >= 75,000/mcL Hemoglobin: >= 8 g/dL total bilirubin: If cirrhosis present: Part of Child Pugh requirement If no cirrhosis: bilirubin should be <= 1.5 x ULN ALT or AST: <= 5 x ULN. Creatinine: < 1.5x institution upper limit of normal OR Measured or calculated creatinine clearance (CrCl): >= 50 mL/min/1.73 m^2 for participant with creatinine levels (eGFR may also be used in place of CrCl) (A): >= 1.5 X institutional ULN ALT (SGPT)=alanine aminotransferase (serum glutamic pyruvic transaminase); AST (SGOT)=aspartate aminotransferase (serum glutamic oxaloacetic transaminase); GFR=glomerular filtration rate; ULN=upper limit of normal. (A)Creatinine clearance (CrCl) or eGFR should be calculated per institutional standard. - Normal cardiac ejection fraction (>= 50% by echocardiogram) and no evidence of hemodynamically significant pericardial effusion as determined by an echocardiogram within 4 weeks before treatment initiation. - Room air oxygen saturation of 92% or greater. - Treatment-related toxicities must be resolved to <= grade 1. - For participants with brain metastases: Participants with <=3 (three or fewer) brain metastases that have been treated with surgery or stereotactic radiosurgery or other form of treatment are eligible. Lesions that have been treated with stereotactic radiosurgery must be clinically stable for one month before protocol treatment. - The study drugs are harmful to developing human fetus. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) at the study entry, for the duration of study therapy, and up to 180 days after the last dose of the study drug(s). Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. - HBV infected participants must be on antivirals and have HBV DNA < 100IU/mL. HCV infected participants can be enrolled with close HCV RNA level monitoring. - Participants must be able to understand and be willing to sign a written informed consent. - For participants that do not have a legally authorized representative in place, one must be identified before study treatment starts EXCLUSION CRITERIA: - Prior systemic therapy, an investigational therapy, radiation, and/or surgery within 4 weeks prior to treatment initiation. - Prior administration of anti-PD-1 or anti-PD-L1 antibodies or other agents that in the opinion of the PI can stimulate immune activity and interfere with an infusion of CAR-T cells within 8 weeks prior to treatment initiation. - Child-Pugh class B or C liver function - Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Note: Participants with a history of abnormal pulmonary function tests but stable obstructive or restrictive pulmonary disease may be eligible per PI discretion. - Participants who require anticoagulation (e.g. warfarin) or anti-platelet therapy (e.g. aspirin > 325 mg/day or clopidogrel). - Any form of primary immunodeficiency (e.g. severe combined immunodeficiency). - HIV-positive participants are excluded because HIV causes complicated immune deficiency and study treatment can pose more risks for these participants. - Participants with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids. These include but are not limited to participants with a history of immune-related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome or CIDP, myasthenia gravis; systemic autoimmune diseases such as SLE, connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn s, ulcerative colitis, hepatitis; and participants with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome. --NOTE: participants with vitiligo, endocrine deficiencies including thyroiditis managed with replacement hormones including physiologic corticosteroids are eligible. Participants with rheumatoid arthritis and other arthropathies, Sjogren s syndrome, and psoriasis controlled with topical medication and participants with positive serology, such as antinuclear antibodies (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ involvement and the potential need for systemic treatment but should otherwise be eligible. - History of severe immediate hypersensitivity reaction to cyclophosphamide or fludarabine. - Hospitalization within 7 days prior to treatment initiation. - Systemic corticosteroid therapy of any dose within 14 days prior to the treatment initiation. Corticosteroid creams, ointments, and eye drops are allowed. - Pregnant women are excluded from this study because study therapy can cause fetal harm. Because there is a potential risk for adverse events in nursing infants secondary to treatment of the mother with study therapy, breastfeeding should be discontinued if the mother is treated with study drugs. - Participants who received live or attenuated vaccine or virus-based vaccine within 30 days before initiation of study therapy - Participants with a history of seizure disorder - Participants with an expected life expectancy of less than 3 months before initiation of study therapy.