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

Background: * Non-small cell lung cancer (NSCLC), which encompasses three main histological subtypes (adenocarcinoma, squamous cell, large cell), accounts for approximately 85% of lung cancers. * Immunotherapy is utilized in the neoadjuvant and adjuvant settings for resectable NSCLC and is an integral component of frontline therapy for patients with metastatic disease. However, less than 50% of patients with advanced-stage NSCLC respond to immune checkpoint inhibitors (ICIs). * Among men in the United States, prostate cancer (PC) is the second leading cause of cancer-related mortality. Though androgen deprivation therapy (ADT) is highly effective for advanced-stage PC, most patients will progress to castration resistance. * Prostate cancer is considered an immunologically "cold" tumor, limiting the effectiveness of immunotherapy alone. However, combining immune checkpoint inhibitors with other systemic treatments - such as androgen receptor-targeting agents, additional ICIs, or targeted therapies like olaparib -may enhance therapeutic efficacy in patients with advanced or aggressive disease. * Thymic epithelial tumors (TETs) are rare cancers with an annual incidence of 0.48 (for thymic carcinomas \[TC\]) to 2.2 (for thymomas) per million individuals in the United States. These tumors are characterized by a low tumor mutation burden, a lack of actionable genomic changes, and defects in immune tolerance. * A subset of patients with TETs treated with ICIs derive durable clinical benefit, and longer survival is observed in patients achieving an objective response as compared to those with stable disease (SD). * STAR0602 is a fully human, bifunctional antibody that binds to Vbeta6/Vbeta10 T-cell receptors (TCRs) promoting the activation and expansion of predominantly CD8+ Vbeta6/Vbeta10 T cells with augmented cytotoxic function and a central memory-like T cell (TCM) phenotype and upregulation of IL-2 receptor (IL-2R) alpha chain. * Nivolumab is a monoclonal antibody against PD-1 which has shown an acceptable tolerability profile and antitumor activity in multiple solid tumors. * STAR0602 may offer a safe and effective therapeutic option for patients who progress after treatment with checkpoint inhibitors (CPIs). Further, preclinical data suggest that objective response and possibly overall survival may be enhanced through use of combination therapy whereby STAR0602 is administered before an anti- programmed cell death protein 1 (PD-1) therapy, such as nivolumab. Objectives: * Phase Ib: To determine the safety of STAR0602 monotherapy in participants with thymic carcinoma (TC), and safety of STAR0602 in combination with nivolumab in participants with non-small cell lung cancer (NSCLC) with or without targetable genomic alterations or metastatic castrate-resistant prostate cancer (mCRPC) * Phase II: To determine the clinical efficacy of STAR0602 alone in participants with TC measured by progression-free survival (PFS) Eligibility: * Age \>=18 years * Histologically or cytologically confirmed diagnosis of NSCLC, mCRPC, or TC * Participants should have at least one measurable lesion. * Eastern Cooperative Oncology Group (ECOG) performance status \<=2 Design: * This is an open label, nonrandomized Phase Ib/II study assessing the safety and clinical activity of STAR0602 monotherapy in participants with TC, and STAR0602 with nivolumab in participants with NSCLC or mCRPC. * Participants with TC will receive STAR0602 by intravenous (IV) infusion on Day 1 and 15 of every 28-day cycle. * Participants with NSCLC or mCRPC will receive STAR0602 and nivolumab by intravenous (IV) infusion on Day 1 and 15 of every 28-day cycle with the exception of Cycle 1 where nivolumab will be only administered on Day 15. * Participants will receive STAR0602 for up to 24 months (24 cycles) and nivolumab for up to 6 months (6 cycles), or until disease progression or development of intolerable adverse events, whichever occurs first. * Up to 52 evaluable participants will be enrolled.