ACTengine® IMA203 Combined With mRNA-4203

Inclusion Criteria: * Pathologically confirmed and documented cutaneous melanoma (CM) or synovial sarcoma (SS) with unresectable or metastatic disease * HLA-A\*02:01 positive * Adequate selected organ function per protocol * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST 1.1) * Life expectancy more than 5 months * CM participants who must have disease progression (resistance, toxicity) on or after at least one PD-1 inhibitor * SS participants must have received (or declined) at least one line of treatment (including SoC) and are still in need of further systemic therapy. * Female participants of childbearing potential must use adequate contraception prior to trial entry until 12 months after the infusion of IMA203 and 15 days after the last mRNA 4203 dose administration Other protocol defined inclusion criteria could apply Exclusion Criteria: * History of other malignancies (except for adequately treated basal or squamous cell carcinoma or carcinoma in situ) within the last 3 years * Pregnant or breastfeeding * Serious autoimmune disease * History of cardiac conditions as per protocol * Prior allogenic stem cell transplantation or solid organ transplantation * Concurrent severe and/or uncontrolled medical disease that could compromise participation in the study * History of hypersensitivity to cyclophosphamide, fludarabine, or IL-2 * History of hypersensitivity to mRNA-based medicines * Positive for HIV infection or with active hepatitis B virus (HBV) or active hepatitis C virus (HCV) infection * Any condition contraindicating leukapheresis * Participants with lactate dehydrogenase (LDH) greater than threshold allowed per protocol * Participants with active brain metastases prior to lymphodepletion * Concurrent treatment in another clinical trial or a device trial that could interfere with the IMA203 treatment * Participants with renal impairment AND reduced bone marrow reserve per protocol Other protocol defined exclusion criteria could apply