General Inclusion Criteria  Applicable to all patients in both the Phase 1 and Phase 2a parts of the study:  Histological or cytologically confirmed locally advanced or metastatic solid tumor Life expectancy >12 weeks. Age ≥18 years. ECOG performance status 0 or 1 at screening. Fully vaccinated against COVID-19 at least 3 weeks before C1D1. If under consideration for a booster, the booster administration needs to be complete within the same time constraint (ie, at least 3 weeks before C1D1).  Adequate organ function, defined as:  Hematology: defined as absolute neutrophil count (ANC) ≥1.5×109/L, platelet ≥90×109/L, hemoglobin ≥9.0 g/dL (in the absence of transfusion and use of growth factors within the last 14 days of screening labs). Renal function defined as calculated creatinine clearance (CCr) or radioisotope glomerular filtration rate >60 mL/min/1.73 m2 calculated by Cockcroft-Gault formula or normal serum creatinine with a maximum serum creatinine of 1.5 mg/dL.  Hepatic Function:  Alanine aminotransferase (ALT) ≤2.5 × ULN; ≤5 × ULN if with liver metastases. Total bilirubin ≤1.5×ULN.  Serum Electrolytes:  Serum potassium, calcium, magnesium, and phosphate within normal limits or not worse than CTCAE v5.0 Grade 1 and asymptomatic. If values are low on the initial screening assessment, supplements may be given, if clinically appropriate, and values repeated to confirm within CTCAE v5.0 Grade 1 limits.  Specific criteria for Phase 1:  Positive claudin 18.2 tumor expression defined as ≥50% of tumor cells demonstrating moderate-to-strong membranous staining (2+/3+) by IHC assay performed on sections of tumor derived from formalin fixed paraffin block. Pathological diagnosis (histological) of any solid tumor cancer with positive claudin 18.2 tumor expression as defined above.  Specific criteria for Phase 2a:  Positive claudin 18.2 tumor expression defined as ≥70% of tumor cells demonstrating moderate-to-strong membranous staining (2+/3+) by IHC assay performed on sections of tumor derived from formalin fixed paraffin block. At least 1 measurable target lesion as defined by RECIST 1.1  Disease progression or relapse following conventional chemotherapy, patient must have documented radiological progression during or after their most recent anticancer therapy:  Pancreatic cancer: Patient should have received at least one but no more than two systemic therapies for their metastatic diseases Gastric cancer (including GEJ cancer): Patient should have received at least two but no more than three systemic therapies for their metastatic diseases; Other solid tumor cancers: Patients with other solid tumors who have no standard therapies available  Exclusion Criteria  Patients who meet any of the following criteria will be excluded:  History of severe infusion reaction with monoclonal antibody treatment. Active or latent hepatitis B or active hepatitis C (test within 8 weeks of screening), or any uncontrolled infection at screening. Known history of HIV. Serious active infection at the time of treatment, or another serious underlying medical condition that would impair the ability of the patient to receive protocol treatment. Presence of other active cancers, or history of treatment for invasive cancer ≤3 years. Patients with Stage I cancer who have received definitive local treatment and are considered unlikely to recur are eligible. All patients with previously treated in situ carcinoma (ie, noninvasive) are eligible, as are patients with history of nonmelanoma skin cancer. Psychological, familial, sociological, or geographical conditions that do not permit compliance with the protocol. Active central nervous system (CNS) disease involvement, defined by cerebrospinal fluid (CSF) cytology, magnetic resonance imaging (MRI) or computerized tomography (CT); patients with asymptomatic CNS metastases are eligible if they have been clinically stable for at least 4 weeks prior to the first dose of study drug and do not require interventions such as surgery, radiation or any corticosteroid therapy for management of symptoms related to CNS disease. Pregnant or nursing (lactating) women (Appendix B). Patients who received claudin 18.2 targeting agents previously.  Prior radiotherapy:  Non-CNS site of radiation must be completed >2 weeks prior to FL-301 infusion CNS directed radiation must be completed >4 weeks prior to FL-301 infusion as long as patients are asymptomatic post radiation therapy