Inclusion Criteria:  Participants must have histologically or cytologically confirmed prostate cancer (code 10036910) with progressive disease at the time of study entry by either  Sequence of at least 2 rising PSA values at a minimum of 1-week intervals Radiographic progression per RECIST1.1 for soft tissue and/or per PCWG3 for bone, with or without PSA progression  Patients must have metastatic disease by bone scintigraphy or other nodal or visceral lesions on CT or MRI with a bone or soft tissue lesion amenable to image-guided percutaneous biopsy, a castrate level of testosterone (<50ng/dL), and evaluable for disease response by either  Baseline PSA ≥ 2.0 ng/mL OR Measurable disease per RECIST 1.1 NOTE: Subjects must maintain a castrate state. If they have not had an orchiectomy, they must continue to receive LHRH or GnRH agonists or antagonists unless intolerant. Past progression on at least one novel hormonal therapy (abiraterone, enzalutamide, apalutamide, darolutamide, galeterone, orteronel, seviteronel or equivalent) in either the hormone-sensitive or castration-resistant disease setting.  Not a candidate for docetaxel or cabazitaxel chemotherapy due to:  progression within 12 months of completion or intolerance to prior taxane OR refusal of taxane OR contraindication to, or lack of fitness for taxane OR investigator assessment that taxane is not clinically indicated or preferred Age ≥18 years. Children under 18 are excluded from this study as prostate cancer is a disease of adults ECOG performance status ≤1 (Karnofsky ≥70%, see Appendix A).  Participants must have adequate organ and marrow function as defined below:  leukocytes ≥ 3,000/mcL absolute neutrophil count ≥1,500/mcL hemoglobin ≥9 g/dL (without transfusion or growth factor in prior 28 days) platelets ≥ 100,000/mcL (without transfusion of growth factor in prior 28 days) total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN) unless known or suspected Gilbert syndrome AST(SGOT)/ALT(SGPT) ≤ 3 × institutional ULN glomerular filtration rate (GFR) ≥60 mL/min/1.73 m2 (based on Cockcroft-Gault formula OR creatinine clearance based on 24 hour urine collection) Human immunodeficiency virus (HIV)-infected participants on effective anti-retroviral therapy (with no known or predicted drug-drug interactions with talazoparib and/or tazemetostat) with undetectable viral load within 6 months are eligible for this trial. For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable. If suppressive therapy is indicated, there must be no known or predicted drug-drug interactions with talazoparib and/or tazemetostat. Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. For participants with HCV infection who are currently on treatment, they are eligible if there are no known or predicted drug-drug interactions with talazoparib and/or tazemetostat and they have an undetectable HCV viral load. Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, participants should be class 2B or better. Prior treatment with a PARP inhibitor is allowed. Planned to undergo core biopsy of a recurrent/metastatic lesion adequate for next generation sequencing (NGS) after trial registration but prior to cycle 1 day 1 of therapy. Confirmation of adequacy of this biopsy material for NGS is NOT required for initiation of therapy. If elective biopsies are not being performed at the treating institution due to preparations or precautions related to COVID-19, this requirement can be waived on discussion with the trial PI. Willing to undergo core biopsy of a recurrent/metastatic lesion adequate for next generation sequencing (NGS) after 8 weeks (+/- 7 days) of study treatment. The effects of talazoparib and tazemetostat on the developing human fetus are unknown. For this reason and because oral chemotherapeutic agents are known to be teratogenic, men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 6 months after completion of talazoparib and tazemetostat administration. Ability to swallow oral medications. Ability to understand and the willingness to sign a written informed consent document.  Exclusion Criteria:  Participants who have had chemotherapy, intravenous experimental agent, radiopharmaceutical therapy or radiotherapy within 4 weeks prior to planned cycle 1 day 1 of study treatment. Participants who have received oral anti-neoplastic intervention such as an oral hormonal agent, PARP inhibitor, or oral experimental agent within 14 days prior to planned cycle 1 day 1 of study treatment. Participants who have not recovered from clinically significant adverse events due to prior anti-cancer therapy (i.e., have clinically significant residual toxicities > Grade 1) except for stable complications of prior procedures (such as urinary incontinence or erectile dysfunction) or Grade 2 anorexia, alopecia, neuropathy, and fatigue, for which resolution is not required. Participants who are receiving any other investigational agents. Participants previously treated with an inhibitor of EZH2. Patients with known brain metastases or leptomeningeal disease should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. History of allergic reactions attributed to compounds of similar chemical or biologic composition to talazoparib or tazemetostat.  Participants receiving the following concurrent medications:  Participants receiving the P-gp inhibitors amiodarone, carvedilol, clarithromycin, itraconazole, or verapamil are ineligible. Participants receiving other P-gp inhibitors are not excluded but should be monitored for potential increased adverse reactions. Participants receiving BCRP inhibitors are not excluded but should be monitored for potential increased adverse reactions. Participants receiving any medications or substances that are strong or moderate inhibitors or inducers of CYP3A4 are ineligible. Precaution is warranted with concomitant use of agents with a narrow therapeutic index that are substrates of CYP3A4 and/or P-gp.  Because the lists of these agents are constantly changing, it is important to regularly consult a frequently updated medical reference. As part of the enrollment/informed consent procedures, the participant will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the participant is considering a new over-the-counter medicine or herbal product.  Participants with uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac arrhythmia. Participants with psychiatric illness/social situations that would limit compliance with study requirements. Pregnant and nursing women are excluded from this study because they do not develop prostate cancer. Arterial or venous thromboembolic event within the last 3 months. Concurrent active malignancy. Patients with non-melanomatous skin cancer, superficial bladder cancer, cancer not needing active therapy for at least 2 years, cancer for which the treating investigator deems the subject to be in remission, or any prior malignancy that was treated with curative intent (no evidence of disease for at least 3 years) are also permitted to enroll.