STAR0602 With Nivolumab in Non Small Cell Lung Cancer and in Metastatic Castrate-Resistant Prostate Cancer, and STAR0602 Alone in Thymic Carcinoma

* INCLUSION CRITERIA: * Participants must have histologically or cytologically confirmed NSCLC, mCRPC, or TC (by outside pathology report or via the NCI Laboratory of Pathology \[LP\]) that is unresectable, locally-advanced, or metastatic, and for which standard curative therapies do not exist or are no longer effective. Progressive disease must be documented prior to study entry. * The following tumor types and prior treatments will be included: * NSCLC: Participants must have received at least one prior approved line of standard therapy. Receipt of prior immune checkpoint inhibitors (ICI) is required unless the participant has a known targetable oncogenic abnormality (e.g., targetable EGFR mutations, KRAS G12C, ALK rearrangement, ROS1 rearrangement, BRAF V600E mutation, NTRK 1/2/3 gene fusion, METex14 skipping mutation, RET rearrangement, ERBB2 \[HER2\], NRG1 gene fusion) that has been treated with appropriate targeted therapy. Prior ICI therapy is not required for participants with NSCLC harboring a targetable oncogenic abnormality. * mCRPC: Participants must have received at least one prior line of treatment with enzalutamide and/or abiraterone with the exception of participants who were treated with docetaxel and androgen deprivation therapy (ADT) for mCRPC and progressed on docetaxel treatment or who progressed within one month of the last docetaxel dose. Participants must agree to continue ADT with a gonadotropin-releasing hormone analogue/antagonist or bilateral orchiectomy. * TC: Participants should have received at least one prior line of standard therapy such as platinum-based chemotherapy. For participants who refuse cytotoxic chemotherapy, a rationale for refusal to receive standard first-line therapy will be captured in the case report form and the medical record. Receipt of prior ICI is permitted. * Presence of \>= 1 measurable lesion by Response Evaluation Criteria in Solid Tumors (RECIST) * Age \>=18 years * Eastern Cooperative Oncology Group (ECOG) performance status \<= 2 * Adequate organ and marrow function as defined below: * Absolute Neutrophil Count (ANC) \>= 1500/mcL * Platelets \>= 75,000/mcL * Hemoglobin (Hgb) \>= 8.5 g/dL * Total bilirubin \<= 1.5 X institutional upper limit of normal (iULN), except participants with Gilbert s syndrome, who may be enrolled if the conjugated bilirubin is within normal limits. * Aspartate aminotransferase (AST) \<= 3 X iULN -OR- \<= 5 X ULN for participants with documented metastatic liver disease * Alanine aminotransferase (ALT) \<= 3 X iULN -OR- \<= 5 X ULN for participants with documented metastatic liver disease * Creatinine clearance \>= 50 mL/min calculated using estimated glomerular filtration rate (eGFR) * Castrate testosterone level (\<50 ng/dl or 1.7 nmol /L) (in participants with mCRPC only) * Participants with symptomatic central nervous system (CNS) metastases must have been treated, be asymptomatic for \>= 14 days, are not receiving concurrent treatment for CNS disease (e.g., surgery, radiation, corticosteroids \>10 mg prednisone/day or equivalent), and do not have concurrent leptomeningeal disease or cord compression. Participants with incidentally discovered, asymptomatic CNS metastases that do not require CNS-directed therapy in the judgment of the investigator, are eligible for the trial. * Human immunodeficiency virus (HIV)-infected participants must have CD4+ T cell (CD4+) counts \>= 350 cells/mcL and HIV viral load (VL) \< 400 copies/mL. * Women of child-bearing potential (WOCBP) must agree to use an effective form of contraception (barrier, hormonal, intrauterine device, surgical sterilization, abstinence) while taking study drugs and for 90 days after the last dose of STAR0602 or 5 months after the last dose of nivolumab whichever comes later. A participant may request a male partner to use an effective form of contraception to fulfill this requirement. Men must agree to use an effective method of contraception (barrier, surgical sterilization, abstinence) while taking study drugs and for 90 days after the last dose of STAR0602 or 5 months after the last dose of nivolumab whichever comes later. A participant may request a female partner to use an effective form of contraception to fulfill this requirement. Men should refrain from fathering a child or donating sperm during the same period. * Breastfeeding participants must be willing to discontinue breastfeeding from study treatment initiation through 90 days after the last dose of STAR0602 or 5 months after the last dose of nivolumab whichever comes later. * Participants must be able to understand and willing to sign a written informed consent document. EXCLUSION CRITERIA: * History of allergic reactions attributed to compounds of similar chemical or biologic composition to STAR0602, or other agents used in study. * Detectable acetylcholine receptor autoantibodies or anti-striational antibodies due to the risk of immune myositis (for participants with TC only). * Persisting toxicity related to prior therapy (NCI CTCAE Grade \> 1 or baseline) with the exception of, alopecia, sensory neuropathy Grade \<= 2 and hearing loss Grade \<= 2. Note: Prior ICI-related endocrine abnormalities are permitted regardless of grade if receiving replacement therapy. * Participants with history of prior ICI-related Grade \> 3 pneumonitis, pericarditis, myocarditis, colitis or any neurological or neuromuscular toxicities. * Treatment with \>10 mg per day of prednisone (or equivalent) or other immunesuppressive drugs within 7 days prior to the initiation of study drug (or 5 half-lives of the drug, whichever is shorter). Exceptions will be made for participants who have had an allergic reaction to iodinated contrast media or those receiving hormonal replacement therapy for previously diagnosed endocrinopathies. Steroids for topical, ophthalmic, inhaled, or nasal administration are allowed. * Participants receiving any other investigational agents. * Prior therapy within the following timeframe with: * Cytotoxic chemotherapy, ICI, small molecule inhibitors, radiation, interventional radiology procedure, or similar investigational therapies within 2 weeks prior to the initiation of study drug(s); * Monoclonal antibodies (except ICIs), antibody-drug conjugates, radioimmunoconjugates, or similar investigational therapies within 6 weeks prior to the initiation of study drug. Note: Concurrent use of hormones for non-cancer-related conditions (e.g., insulin for diabetes, hormone replacement therapy) or use of gonadotropin-releasing hormone analogue/antagonist for androgen deprivation in mCRPC is acceptable. Bisphosphonates or denosumab are permitted for supportive care of bone metastases. Palliative radiotherapy is permitted to non-target lesions. * Known autoimmune disease except for: * Vitiligo * Psoriasis, atopic dermatitis, or other autoimmune skin condition not requiring systemic treatment * Endocrinopathies managed by endocrine replacement therapy * Alopecia * Arthritis managed without systemic therapy beyond oral nonsteroidal anti-inflammatory drugs * TC-associated paraneoplastic syndromes that do not require systemic immunosuppressive therapy * Active second malignancy within the past 12 months, except for basal or squamous cell carcinoma of the skin, cervical carcinoma in situ, ductal carcinoma in situ of the breast, papillary or follicular thyroid carcinoma, non-muscle invasive bladder cancer and any malignancy that has been definitively/curatively treated without evidence of relapse. * Participants must not have received major surgeries within 4 weeks prior to the first study drug administration. * Active infection requiring systemic therapy or significant acute or chronic infections including, among others, hepatitis B virus (HBV) or hepatitis C virus (HCV) infection (positive HBV surface antigen \[HBsAg\] or HCV RNA if anti-HCV antibody test is positive) * Vaccination with any live virus vaccine within 4 weeks before the initiation of study drug administration. * Positive serum or urine beta-human chorionic gonadotropin (beta-hCG) test at screening (WOCBP only) * Severe uncontrolled intercurrent illness as evaluated by history, physical exam, electrocardiogram (EKG) and labs that would unacceptably increase risk for the participant or impair the ability to evaluate the endpoints of the study.