A Study of a Selective T Cell Receptor (TCR) Targeting, Bifunctional Antibody-fusion Molecule STAR0602 in Participants With Advanced Solid Tumors

Inclusion Criteria: 1. Participants must have histologically confirmed solid tumors that are unresectable, locally advanced, or metastatic and for which standard curative therapies do not exist or are no longer effective or have intolerable toxicities. Participants should not have received more than three regimens of prior therapies for their advanced or metastatic diseases. For Phase 2 Cohorts 8 and 10 (see below), participants should not have received more than one line of prior therapy. 2. For Phase 1, participants must have one of the following solid tumors: 1. High mutational burden (TMB-H) 2. Microsatellite Instability (MSI-H)/DNA mismatch repair (dMMR) 3. Virally associated tumors 4. Solid tumors generally considered as immunogenic (e.g., melanoma and renal cell carcinoma) are eligible without prior testing for TMB, MSI or viral status after the Sponsor's approval. 3. For Phase 2, participants must have one of the following solid tumors: 1. TMB-H (not enrolling) 2. MSI-H/dMMR (not enrolling) 3. CRC (both Ras wild type and mutant) (not enrolling) 4. NSCLC (recurrent or Primary Stage 4) 5. CRC with pMMR/MSS (without TMB-H requirement) (Other tumor histologies may also be included in Phase 2 as additional data emerge to support their inclusion.) 4. Symptomatic central nervous system (CNS) metastases must have been treated, be asymptomatic for ≥ 14 days, and meet the following at the time of enrollment: * No concurrent treatment for CNS disease (e.g., surgery, radiation, corticosteroids \> 10 mg prednisone/day or equivalent); * No concurrent leptomeningeal disease or cord compression. 5. Subjects who have previously received a CPI (e.g., anti-PD-L1, anti-PD-1, anti CTLA 4) prior to enrollment must have CPI immune-related toxicity resolved to either Grade ≤ 1 or baseline (prior to the CPI) to be eligible for enrollment. * Subjects who experienced previous CPI-related endocrine abnormalities are eligible for the study regardless of CTCAE grade if well controlled on replacement therapy. * Subjects who have had previous CPI-related Grade 3 to 4 pneumonitis, peri/myocarditis, colitis and bowel perforation, myositis, encephalitis, or peripheral neuropathy will need Sponsor approval. Exclusion Criteria: 1. Participants with a history of known autoimmune disease with exceptions of: * Vitiligo; * Psoriasis, atopic dermatitis or other autoimmune skin condition not requiring systemic treatment; * History of Graves' disease, now euthyroid for \> 4 weeks; * Hypothyroidism managed by thyroid replacement; * Alopecia; * Arthritis managed without systemic therapy beyond oral nonsteroidal anti-inflammatory drugs. * Adrenal insufficiency well controlled on replacement therapy. 2. Major surgery or traumatic injury within 8 weeks before first dose of study drug. 3. Unhealed wounds from surgery or injury. 4. Treatment with \>10 mg per day of prednisone (or equivalent) or other immune-suppressive drugs within 7 days prior to the initiation of study drug. Exceptions may be made for patients who have had allergic reaction to iodinated contrast media. Steroids for topical, ophthalmic, inhaled, or nasal administration are allowed. 5. Prior therapy within the following timeframe before planned infusion of STAR0602 as follows: * Cytotoxic chemotherapy, small molecule inhibitors, radiation, interventional radiology procedure, or similar investigational therapies within ≤ 2 weeks or participants who have not recovered (i.e., ≤ Grade 1 or to baseline) from AEs due to a previously administered agent; * Monoclonal antibodies, antibody-drug conjugates, radioimmunoconjugates, or similar investigational therapies within 6 weeks prior to the initiation of study drug or participants who have not recovered (i.e., ≤ Grade 1 or to baseline) from AEs due to agents administered more than 4 weeks earlier. Note: Participants with ≤ Grade 2 neuropathy or ≤ Grade 2 alopecia are an exception to this criterion and may qualify for the study. 6. Clinically significant cardiovascular/vascular disease, gastrointestinal disorders, inflammatory processes, pulmonary compromises 7. Active viral, bacterial, or systemic fungal infection requiring parenteral treatment within 7 days prior to the initiation of study drug. 8. Vaccination with any live virus vaccine within 4 weeks prior to the initiation of study drug administration. Inactivated annual influenza vaccination is allowed. 9. Participants who are known to be human immunodeficiency virus positive or hepatitis B or C positive and have uncontrolled disease. 10. Second primary invasive malignancy not in remission for ≥ 1 year. Exceptions include non-melanoma locally advanced skin cancer, cervical carcinoma in situ, localized prostate cancer (Gleason score ≤ 7), resected melanoma in situ, or any malignancy considered to be indolent and never required systemic therapy, with the exception of indolent lymphomas. 11. Pregnant, likely to become pregnant, or lactating women (where pregnancy is defined as the state of a female after conception and until the termination of gestation). 12. Hepatic metastases unless adequately treated, either locally (e.g., by surgery, radiofrequency ablation, or chemoembolization) or systemically or both, and stable for 3 months. 13. Bulky disease defined as any lesion ≥ 5 cm in greatest dimension unless approved by the Sponsor.