A Clinical Study of TJ004309 With Atezolizumab (TECENTRIQ®) in Patients With Ovarian Cancer and Selected Solid Tumors

Inclusion Criteria: * Cohort 1: Patients with histologically confirmed epithelial ovarian cancer, fallopian tube, or primary peritoneal cancer subjects with any high-grade serous component, progressed on or after platinum-containing therapy and not eligible for further platinum containing treatment (platinum-resistant, platinum-refractory disease defined by progression of disease on a platinum-containing regimen or recurrence of disease within 180 days of receiving the last dose of platinum-based treatment). * Cohort 2: Patients with selected tumor types that have relapsed or progressed after 2 lines of therapy or who are ineligible for other standard of care (SOC) therapies: 1. Histologically or cytologically confirmed metastatic NSCLC 2. Histologically or cytologically confirmed recurrent or metastatic HNSCC (oral cavity, oropharynx, hypopharynx, or larynx) 3. Histologically or cytologically confirmed metastatic or non-resectable advanced metastatic gastric or gastroesophageal adenocarcinoma 4. Histologically or cytologically confirmed unresectable, locally advanced or metastatic TNBC (confirmed HER2-negative, estrogen receptor-negative and progesterone receptor-negative) 5. Histologically confirmed ovarian cancer of all high-grade epithelial types who are IO treatment naïve and have progressed after 3 months on or after platinum-containing therapy 6. PD-L1 expression Tumor Proportion Score (TPS) ≥ 1% for NSCLC and Combined Proportion Score (CPS) ≥ 1% for all other tumor types 7. A 28-day washout period after the completion of programmed death-1 (PD-1)/PD-L1 therapy 8. Patients should have no more than 5 prior lines of therapies * Cohort 2 - (Optional for the ovarian cohort) Pre-treatment fresh tumor biopsies and paired treatment fresh tumor biopsies will be collected from at least 5 patients. Biopsy must be excisional, incisional, or core. Exclusion Criteria: * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g. cytotoxic T-lymphocyte-associated protein 4 \[CTLA-4\], OX 40 \[Tumor necrosis factor receptor superfamily, member 4 (TNFRSF4)\], CD137 \[tumor necrosis factor receptor superfamily member 9 (TNFRSF9)\]) (only applies to ovarian cancer patients in Cohorts 1 and 2) * Disease progression within 3 months of starting anti-PD-1 and anti-PD-L1 inhibitors * Known active or chronic Hepatitis B or Hepatitis C, other hepatitides (non-alcohol steatohepatitis, alcohol or drug-related, autoimmune) serology at screening or cirrhosis * Active autoimmune disease requiring systemic treatment within the past 12 months * Active interstitial lung disease (ILD) or pneumonitis or a history of ILD * Brain involvement with cancer, spinal cord compression, carcinomatous meningitis, or new evidence of brain or leptomeningeal disease; unless the lesion(s) have been radiated or resected, are considered fully treated and inactive, are asymptomatic, and no steroids have been administered for CNS disease over the 7 days prior to study treatment * Angina, myocardial infarction (MI), symptomatic congestive heart failure, cerebrovascular accident, transient ischemic attack TIA), arterial embolism, pulmonary embolism, percutaneous transluminal coronary angioplasty (PTCA), or coronary artery bypass grafting (CABG) within 6 months prior to study treatment * Known human immunodeficiency virus (HIV) unless CD4+ T cell count \> 350 cells/μL with an undetectable viral load