GPC3 Targeted CAR-T Cell Therapy in Advanced GPC3 Expressing Solid Tumor Malignancies

Background: * Hepatocellular carcinoma (HCC) is the fifth most common cancer worldwide and the second leading cause of cancer-associated mortality with an average life expectancy of 6-9 months * Despite the success of several studies showing efficacy in treating HCC, most clinical trials have failed to prove a survival advantage. * Adoptive T-cell therapy exploits the natural ability of T-cells to recognize and eliminate their target. * GPC3 is a cell surface protein that is expressed in nearly all HCC yet is undetectable in normal adult hepatic tissues. * GPC3 is also expressed strongly in some non-HCC solid tumor malignancies. * We want to evaluate the role of GPC3 targeted chimeric antigen receptor (CAR)-T cells in advanced GPC3 expressing HCC as well as other advanced solid tumor malignancies with GPC3 expression. Objective: -To determine the safety and feasibility of T-cells, expressing a novel humanized anti-GPC3 chimeric antigen receptor, in participants with advanced solid tumor malignancy, expressing GPC3. Eligibility: * Histologically confirmed diagnosis of hepatocellular carcinoma or other solid tumor malignancy. * GPC3 positivity of \>= 25% by immunohistochemistry * At least 1 measurable lesion by RECIST v 1.1 criteria * Age \>= 18 years Design: * We plan to conduct a phase I dose escalation designed clinical trial using CAR (hYP7)-T cells in participants with advanced hepatocellular carcinoma or other advanced solid tumor malignancy, expressing GPC3. * Participants will undergo leukapheresis * Participants will receive a lymphocyte depleting chemotherapy conditioning regimen with the intent of enhancing the activity of the infused CAR-expressing T cells * Following the T cell infusion, there is a mandatory 9-day inpatient hospitalization to monitor for toxicity. * The participants will be closely monitored during the first year after cell infusion and followed for life.