Talazoparib in Combination With Belinostat for Metastatic Breast Cancer, Metastatic Castration Resistant Prostate Cancer, and Metastatic Ovarian Cancer

Inclusion Criteria: * One of the following disease types: Men or women with histologically confirmed metastatic or unresectable breast cancer that is HER2 negative as assessed by 2018 ASCO-CAP guidelines. Trial participants with hormone receptor positive disease must have progression on at least one hormonal therapy and a CDK inhibitor AND be considered a candidate for chemotherapy; OR, Men with metastatic castration resistant prostate cancer with progression on androgen deprivation therapy and at least one additional agent in the metastatic setting; OR, Women with metastatic high grade serous ovarian cancer with progression on at least one chemotherapy agent; OR, men or women with metastatic or unresectable pancreatic adenocarcinoma with progression on at least one chemotherapy regimen in the metastatic/unresectable setting * Measurable disease as defined by RECIST 1.1 criteria. * Trial participants must be at least 21 days from last dose of chemotherapy and recovered from all chemotherapy-related reversible toxicity to Grade 0 or 1, with the exception of alopecia and neuropathy. * The last radiation therapy (including palliative radiation) must have occurred ≥3 weeks prior to study registration. * Trial participants must have experienced disease progression at the time of study enrollment. * ECOG performance status of 0 or 1. * Adequate organ and marrow function per protocol. * Trial participants with treated brain metastases are eligible provided the metastases are recently treated and/or clinically stable and greater than 4 weeks has elapsed from time of treatment and date of initiation of study drug. * Trial participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen should be included. * Males and females of reproductive potential must use two forms of effective contraception during the duration of the trial and for minimum of 7 months after last dose of study drug. A woman of reproductive potential is defined as a premenopausal female with intact uterus and ovaries. For women, non-childbearing potential is defined as: * ≥45 years of age and has not had menses for \>2 years. * Amenorrheic for \<2 years without a hysterectomy and oophorectomy and a follicle-stimulating hormone value in the postmenopausal range upon pre-study (screening) evaluation. * Post hysterectomy, oophorectomy or tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure. * Ability to understand and the willingness to sign a written informed consent. Exclusion Criteria: * Previous or current treatment with a histone deacetylase inhibitor (HDACi)S. * Participation in other investigational studies concurrently if these therapies include a therapeutic intervention. * Treatment with any investigational agent within 30 days (or 5 serum half-lives of the investigational drug, whichever is longer) of enrollment. * Evidence of current serious uncontrolled concomitant cardiovascular nervous system, pulmonary (including obstructive pulmonary disease), renal, hepatic, endocrine (include uncontrolled diabetes mellitus) or gastrointestinal disease. * History or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the patient's participation for the full duration of the study, or is not in the best interest of the patient to participate, in the opinion of the treating Investigator, including, but not limited to: * Myocardial infarction or arterial thromboembolic events within 6 months prior to screening or severe or unstable angina, New York Heart Association (NYHA) Class III or IV disease, or a QTc interval \> 450 msec. * Uncontrolled hypertension or diabetes mellitus. * Another known malignancy that is progressing or requires active treatment. * Active infection requiring systemic therapy. * Known active central nervous system (CNS) metastases and/or carcinomatous meningitis. * Any contraindication to oral agents or significant nausea and vomiting, malabsorption, or significant small bowel resection that, in the opinion of the investigator, would preclude adequate absorption. * Allergy to talazoparib, belinostat or to the inactive components of talazoparib or belinostat formulations. * Pregnancy or breastfeeding. * QTc ≥ 450 ms or congenital long QT syndrome given potential for prolongation with belinostat. * Current or anticipated use within 7 days prior to enrollment, or anticipated use during the study of drugs which are moderate or strong inhibitors of UGT1A1 per protocol. * Current or anticipated use within 7 days prior to enrollment, or anticipated use during the study, of strong P-gp inhibitors per protocol. * Subjects homozygous for UGT1A1\*28 allele; this will be determined via clinical testing by polymerase chain reaction with capillary electrophoresis by the University of Michigan Molecular Diagnostics laboratory. * Any medical or psychological condition that in the opinion of the principal investigator would interfere with safe completion of the trial.