The COSMYC Trial (COmbined Suppression of MYC)

Inclusion Criteria: 1. Eastern Cooperative Oncology Group (ECOG) Performance status ≤2. 2. Age ≥18 years. 3. Histologically-confirmed adenocarcinoma of the prostate. 4. Treated with continuous androgen ablative therapy (either surgical castration or LHRH agonist/antagonist). 5. Documented castrate level of serum testosterone (\<50 ng/dl). 6. Metastatic disease radiographically documented by CT or bone scan. While CT scan is preferred, Prostate-Specific Membrane Antigen (PSMA) scan (e.g. Pylarify) may be substitute for CT scan if evidence of metastatic disease observed on the CT portion of the PSMA scan. 7. Must have had disease progression while on a second-generation AR-axis inhibitor (Abiraterone, Enzalutamide, Darolutamide, or Apalutamide) based on: PSA progression defined as an increase in PSA, as determined by 2 separate measurements taken at least 1 week apart i. And/ Or Radiographic disease progression, based on RECIST 1.1 in patients with measurable soft tissue lesions or PCWG3 for patients with bone disease 8. Screening PSA must be ≥ 1.0 ng/mL. 9. Patients with soft tissue lesion amenable to biopsy must agree to biopsy collection pre-treatment and at a defined point on treatment to perform tumor tissue analysis. 10. Prior treatment with Provenge vaccine, 223 Radium (Xofigo), poly(ADP-ribose) polymerase (PARP) inhibitors, taxane chemotherapy, Pluvicto, antiandrogens (including enzalutamide, darolutamide, and apalutamide), and radiation is allowed if \>4 weeks from last dose. 11. Prior treatment with BAT is allowed if the patient has progressed on an AR-axis inhibitor (i.e. abiraterone or antiandrogen) since BAT treatment. 12. Patients must be withdrawn from second-generation AR-axis inhibitor (Abiraterone, Enzalutamide, Darolutamide, or Apalutamide) for ≥ 2 weeks. 13. Attempts must be made to wean patients off prednisone prior to starting therapy. Patients who cannot be weaned due to symptoms may continue on lowest dose of prednisone achieved during weaning period. 14. Acceptable liver function: 1. Bilirubin \< 2.5 times institutional upper limit of normal (ULN) 2. Aspartate Transferase (AST) (SGOT) and Alanine Transaminase (ALT) (SGPT) \< 2.5 times ULN 15. Acceptable renal function: a. Serum creatinine \<2.5 times ULN 16. Acceptable hematologic status: 1. Absolute neutrophil count (ANC) ≥ 1000 cells/mm3 (1.5 ×109/L) 2. Platelet count ≥ 100,000 platelet/mm3 (100 ×109/L) 3. Hemoglobin ≥ 7.5 g/dL. 17. Ability to understand and willingness to sign a written informed consent document. 18. Sexually active participants with female partners of childbearing potential are eligible to participate if they agree to follow 1 of the following methods of contraception consistently, starting from screening, during the study and for at least 3 months after the last dose of ZEN-3694 and/or enzalutamide: i. Are abstinent from penile-vaginal intercourse as their usual and preferred lifestyle (abstinent on a long-term and persistent basis) and agree to remain abstinent. ii. Are sterilized (with the appropriate post-vasectomy documentation of the absence of sperm in the ejaculate); iii. Agree to use a male condom and have their partner use a contraceptive method with a failure rate of \<1% per year as described below when having penile-vaginal intercourse with a woman of childbearing potential who is not currently pregnant, and who agrees to the use of a condom by her partner. b. In addition, participants must refrain from donating sperm starting from Screening, during the study and for at least 3 months after the last dose of ZEN-3694 and/or enzalutamide. 19. Sexually active participants with a pregnant or breastfeeding partner must agree to remain abstinent from penile-vaginal intercourse; or use a male condom during each episode of penile penetration during the study 20. Patients with soft-tissue disease amenable to biopsy as determined by Interventional Radiology must agree to serial biopsies as per the study schedule to be eligible. Exclusion Criteria: 1. Pain due to metastatic prostate cancer requiring treatment intervention with opioid pain medication. 2. ECOG Performance status ≥3 3. Requirement for urinary self-catheterization for voiding due to obstruction secondary to prostatic enlargement well documented to be due to prostate cancer or benign prostatic hyperplasia (BPH). Patients with indwelling Foley or suprapubic catheter for obstructive symptoms are eligible. 4. Active uncontrolled infection. Patients with a history of HIV/AIDS may be eligible if cluster of differentiation 4 (CD4)+ T cell counts are ≥ 350 cell/ul, they have had no opportunistic infection within the past 12 months, they have been on established antiretroviral therapy (ART) for at least four weeks, the HIV viral load is less than 400 copies/ml prior to enrollment, and there is no significant drug-drug interaction with ART and the study drugs. Patients with chronic hepatitis B virus (HBV) infection with active disease who meet criteria for anti HBV therapy are eligible if they are on a suppressive antiviral therapy prior to enrollment and there is no drug-drug interaction with the study drugs. Patients with a history of HCV infection are eligible if they have completed curative antiviral treatment and the hepatitis C virus (HCV) viral load is below the limit of quantification. 5. Any condition or mental impairment that may compromise the ability to give informed consent, patient's safety or compliance with study requirements as determined by the investigator. 6. Patients receiving anticoagulation therapy with warfarin, rivaroxaban, or apixaban are not eligible for study. \[Patients on enoxaparin or edoxaban are eligible for study. Patients on warfarin, rivaroxaban, or apixaban, who can be transitioned to one of these alternative agents prior to starting study treatments will be eligible\]. 7. Patients are excluded with prior history of a thromboembolic event within the last 12 months that are not being treated with systemic anticoagulation. 8. Hematocrit \>51%, untreated severe obstructive sleep apnea, uncontrolled or poorly controlled heart failure \[per Endocrine Society Clinical Practice Guidelines (34)\] 9. Patients allergic to sesame seed oil or cottonseed oil are excluded. 10. Major surgery (i.e. as defined by treating physician) within 3 weeks before screening, or has not fully recovered from prior surgery (i.e., unhealed wound). Note: subjects with planned surgical procedures to be conducted under local anesthesia may participate. Patients with history of seizure or any condition that may predispose to seizure (e.g., prior cortical stroke or significant brain trauma, brain arteriovenous malformation).