BOXR1030 T Cells in Subjects With Advanced GPC3-Positive Solid Tumors

Inclusion Criteria: 1. Aged 18 to 80 years at time of enrollment 2. Body weight \>/= 50kg 3. Able to provide a recent tumor specimen taken within 6 months prior to signing consent and after the initiation of the subject's most recent systemic anti-cancer therapy, for GPC3 expression assessment by immunohistochemistry (IHC). Previously collected tumor tissue older than 6 months at time of GPC3 IHC testing or collected prior to initiation of current or last systemic therapy may be permitted for GPC3 prescreening. If prescreening sample is found to be GPC3+, a new tumor biopsy will be needed to confirm tumor remains GPC3+ in order to proceed. 4. Histologically confirmed advanced unresectable or metastatic hepatocellular carcinoma (HCC), squamous cell carcinoma (SCC) of the lung, myxoid/round cell liposarcoma (MRCLS), or Merkel cell carcinoma (MCC) with GPC3 overexpression by IHC. Subjects must consent to IHC testing in a separate informed consent. Note: Tumor samples will be sent to a central laboratory for GPC3 expression analysis. 5. Documentation of disease progression or refractory disease or intolerance to prior lines of standard-of-care therapies. Patients with tumors with genetic alterations and mutations (e.g., breast cancer gene, epidermal growth factor receptor mutations, and anaplastic lymphoma kinase translocation) who have approved targeted therapies available for their cancer will need to have been treated with such approved therapies or refused such approved targeted therapy for their cancer prior to enrolling in this study. 6. Life expectancy \>16 weeks 7. Have adequate organ function (renal/hepatic/pulmonary) 8. Left ventricular ejection fraction ≥50% by multiple-gated acquisition scan or echocardiogram 9. Eastern Cooperative Group performance status of 0 to 1 10. For subjects with HCC: * Child-Pugh Score of A * No fibrolamellar carcinoma or mixed hepatocellular cholangiocarcinoma histology * No grade 2 or grade 3 ascites based on the European Association for the Study of Liver guidelines. 11. A minimum of 2 sites of disease, including at least 1 site that is measurable by RECIST 1.1 criteria to ensure sufficient disease for response assessment. At least 1 of the other lesions must be considered adequate for Protocol-required tumor biopsy. 12. Adequate wash-out of prior systemic therapy for underlying malignancy, relative to leukapheresis: * Last dose of any antineoplastic treatment must be at least 2 weeks before leukapheresis. * Last dose of any investigational agent must be at least 3 half-lives of the treatment, or 28 days, before leukapheresis (whichever is shorter). Adequate wash-out of prior systemic therapy for underlying malignancy, relative to LD chemotherapy: Subjects may receive an additional dose of their last received form of therapy at the same dose and dosing schedule following leukapheresis as bridging therapy; however, the required wash-out period prior to start of LD chemotherapy must be adhered to: * The last dose of systemic nitrosourea or systemic mitomycin-C must be at least 6 weeks before the first dose of LD chemotherapy in this study. * For all other systemic cytotoxic chemotherapy, the wash-out must be the duration of a full cycle of that therapy. For example, if the prior therapy is given in 3-week cycles, there must be at least 3 weeks between the last dose of that therapy and the first dose of LD chemotherapy in this study. If the prior therapy is administered more frequently than every 2 weeks, a minimum 2-week wash-out is required. * For biologic therapy (e.g., antibodies) the wash-out must be either the duration of the biologic agent dosing interval, or 3 weeks, whichever is shorter. * For small molecule therapies, the wash-out must be 5 half-lives of the drug. * For any investigational agent, the wash-out must be 3 half-lives of the investigational agent, or 4 weeks, whichever is shorter. Note: Local radiation of lesions is allowed if indicated for palliation requiring 1 week wash-out prior to start of BOXR1030 dosing if \< 2 weeks of radiotherapy for non-central nervous system (CNS) disease; locally treated lesions will be considered non-target lesions. Hormone ablation is also allowed as clinically indicated. Exclusion Criteria: 1. Prior treatment with adoptive cell therapy (e.g., CAR T-cell therapy, natural killer cell therapy, engineered T-cell receptor therapy). 2. History of allogenic hematopoietic stem cell transplant. 3. Known untreated CNS tumors or brain metastasis. Subjects are eligible if CNS metastases are asymptomatic, have been treated with radiotherapy for at least 1 month prior to informed consent, are off corticosteroids and have neurologically returned to baseline (residual signs or symptoms related to the CNS treatment are permitted). Imaging obtained for the purpose of CNS metastases management performed during screening must document radiographic stability of CNS lesions for at least 1 month prior to leukapheresis and be performed after completion of any CNS directed therapy. If brain scans are performed, magnetic resonance scans are preferred; however, computed tomography scans are acceptable if magnetic resonance imaging is medically contraindicated. CNS evaluation for subjects with no suspicion of brain tumors in their history is not required for the study. Subjects with known leptomeningeal metastases are excluded. 4. Subjects who have not recovered to \< 1 or baseline from all AEs due to previous therapies (subjects with ≤ grade 2 peripheral neuropathy that has been stable for at least 4 weeks or \< grade 2 endocrine-related AEs that has been stable for at least 4 weeks on replacement therapy). 5. Planned use of any antineoplastic treatment or investigational agent from the time of the first dose of LD chemotherapy through the end of study participation, except for allowed local radiation of lesions for palliation (to be considered non-target lesions after treatment) and hormone ablation. 6. Uncontrolled or life-threatening symptomatic concomitant disease including clinically significant gastrointestinal bleeding or pulmonary hemorrhage within 4 weeks before screening, known symptomatic human immunodeficiency virus (HIV) positive with an acquired immunodeficiency syndrome-defining opportunistic infection within the past 12 months prior to screening, or a current CD4 count \<350 cells/µL, symptomatic active hepatitis B or C checked at screening, or active tuberculosis therapy. Subjects with HIV are eligible if: * They have received antiretroviral therapy (ART) as clinically indicated for at least 12 months prior to starting LD therapy and have an HIV viral load less than 40 copies/mL prior to start of LD therapy. * They continue on ART as clinically indicated while enrolled on study. * CD4 counts\> 350 cells/µL and CD4 counts and viral load are monitored per standard of care by a local health care provider. * They are fully vaccinated against SARS-CoV-2. 7. Has received prior radiotherapy within 2 weeks of the start of BOXR1030. Subjects must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had severe radiation pneumonitis. 8. Potentially life-threatening second malignancy requiring systemic treatment within the last 3 years (i.e., subjects with a history of prior malignancy are eligible if treatment was completed at least 3 years before entering the Treatment Period and the subject has no evidence of disease) or which would impede evaluation of treatment response. 9. Clinically significant (i.e., active) cardiovascular disease: cerebral vascular accident/stroke (\<6 months prior to enrollment), myocardial infarction (\<6 months prior to enrollment), unstable angina, congestive heart failure (New York Heart Association Classification Class II), or the presence of any condition that can increase proarrhythmic risk (e.g., hypokalemia, bradycardia, heart block) including any new, unstable, or serious cardiac arrhythmia requiring medication, or other baseline arrhythmia that might interfere with interpretation of electrocardiograms on study (e.g., bundle branch block). 10. Has an active infection excluding controlled HIV. 11. Has an active autoimmune disease requiring systemic (immunosuppressive) therapy. NOTE: Additional inclusion/exclusion criteria may apply. The above information is not intended to be an exhaustive list of considerations for potential participation in a clinical trial.