Study of NMS-03305293 in Adult Patients With Relapsed Ovarian Cancer

Inclusion Criteria - * Histologically confirmed diagnosis of high-grade serous epithelial ovarian, fallopian tube or peritoneal cancer. Sponsor might opt to restrict enrollment to either platinum refractory, primary or secondary platinum-resistant patients based on data emerging from the trial. * Patients must have received no more than 5 prior lines of therapy and failed all evidence based local standards of care as per Investigator judgment. Sponsor might opt to restrict prio lines of therapy to 3 in any moments, based on data emerging from the trial. * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2. * Patient must have progressed radiographically on or after their most recent line of anticancer therapy and have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 (radiologically measured by the Investigator). * Resolution of all acute toxic effects (excluding alopecia) of any prior anticancer therapy to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) (version 5.0) Grade ≤ 1 or to the baseline laboratory values as defined in the protocol * Patients with childbearing potential must use highly effective contraception or true abstinence. Exclusion Criteria - * Current enrollment in another interventional clinical trial. * Current treatment with other anticancer agents or devices. * BReast CAncer gene (BRCA) mutation or homologous recombination deficiency. * Prior therapy with PARP inhibitor, outside of approved indication and schedules. Sponsor might opt to restrict prior use of PARP inhibitor (PARPi) in any moments, based on data emerging from the trial. * Prior therapy with topoisomerase inhibitors including payloads of Antibody-Drug Conjugates (ADCs). * Major surgery, other than surgery for recurrent Ovarian Cancer (OC), within 4 weeks prior to treatment start. * Patients with low-grade/borderline ovarian tumor. * Prior anti-tumor treatment within 2 weeks prior to treatment start or 5 half-lives, whichever is longer. * Patients with prior wide-field radiotherapy (RT) affecting at least 20 percent of the bone marrow. * Use of full-dose anticoagulants unless the INR or activated thromboplastin time (aPTT) is within therapeutic limits (according to the medical standard in the institution) and the patient has been on a stable dose of anticoagulants for at least 2 weeks before enrollment. * Treatment with concomitant medications known to be sensitive substrates of CYP2D6 and CYP2C19 that cannot be replaced with another treatment. * History of interstitial lung disease or relevant lung disease in the opinion of the Investigator. * Treatment with systemic immune modulators such as corticosteroids at prednisone equivalent dose of \> 10 mg/day, cyclosporine and tacrolimus or radiotherapy within 28 days before Cycle 1 Day 1. * Pregnant women. All female patients with reproductive potential must have a negative pregnancy test (serum or urine) within the screening period prior to start of study drug. * Breast-feeding women or women planning to breast feed during the study or within 3 months after study treatment. * Known hypersensitivity to any component of NMS-03305293 or topotecan drug formulations. * Known active, life-threatening or clinically significant uncontrolled systemic infection (bacterial, fungal, viral including Human Immunodeficiency Virus (HIV) positivity or Hepatitis B Virus (HBV) or Hepatitis C Virus (HCV) infections) requiring systemic treatment; HIV or AIDS-related illness are allowed as long as controlled more than 6 months to undetectable on anti-HIV medications. * Patients with QTc interval ≥ 450 milliseconds or with risk factors for torsade de pointes (e.g., uncontrolled heart failure, uncontrolled hypokalemia, history of prolonged QTc interval or family history of long QT syndrome). For patients receiving treatment with concomitant medications known to prolong the QTc interval, replacement with another treatment prior to enrollment is mandatory. If concomitant use of anti-emetics is considered essential for the care of the patients, follow instruction in this protocol. * Known active gastrointestinal disease (e.g., documented gastrointestinal ulcer, Crohn's disease, ulcerative colitis, or short gut syndrome) or other malabsorption syndromes or structural issues or ulcer that would impact on drug absorption. * Any of the following in the previous 6 months: myocardial infarction, unstable angina, coronary/peripheral artery bypass graft, symptomatic congestive heart failure, cerebrovascular accident or transient ischemic attack, pulmonary embolism, deep vein thrombosis, active bleeding disorder and interstitial lung disease. * History of long QT disorder or familial sudden death syndromes or related syndromes in the opinion of the Investigator. * Currently active second malignancy, except for adequately treated basal or squamous cell skin cancer and/or cone biopsied or post curative intention in situ carcinoma of the cervix uteri and/or superficial bladder cancer. * Symptomatic, or untreated Central Nervous System (CNS) lesions except stable and well-controlled with no neurological symptoms; patients receiving corticosteroids to control neurological symptoms should be on stable doses for at least 14 days before study entry. * Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation or study drug administration or may interfere with the interpretation of study results and, in the judgment of the Investigator, would make the patient inappropriate for entry into this study or could compromise protocol objectives in the opinion of the Investigator and/or the Sponsor. NOTE: Other protocol defined inclusion and exclusion criteria may apply.