This phase II trial evaluates whether genetic testing in prostate cancer is helpful in deciding which study treatment patients are assigned. Patient cancer tissue samples are obtained from a previous surgery or biopsy procedure and tested for deoxyribonucleic acid (DNA) and ribonucleic acid (RNA) abnormalities or mutations in their cancer. Valemetostat tosylate is in a class of medications called EZH1/EZH2 inhibitors. It blocks proteins called EZH1 and EZH2, which may help slow or stop the spread of tumor cells. Carboplatin is in a class of medications known as platinum-containing compounds. It works in a way similar to the anticancer drug cisplatin, but may be better tolerated than cisplatin. Carboplatin works by killing, stopping or slowing the growth of tumor cells. Cabazitaxel injection is in a class of medications called microtubule inhibitors. It works by slowing or stopping the growth of tumor cells. Abiraterone acetate blocks tissues from making androgens (male hormones), such as testosterone. This may cause the death of tumor cells that need androgens to grow. It is a type of anti-androgen. Enzalutamide is in a class of medications called androgen receptor inhibitors. It works by blocking the effects of androgen (a male reproductive hormone) to stop the growth and spread of tumor cells. Lutetium Lu 177 vipivotide tetraxetan is in a class of medications called radiopharmaceuticals. It works by targeting and delivering radiation directly to tumor cells which damages and kills these cells. Assigning patients to targeted treatment based on genetic testing may help shrink or slow the cancer from growing

The primary and secondary objectives of the study:

PRIMARY OBJECTIVE:

I. Evaluate objective response rate in patients with measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 for measurable disease, in each treatment arm.

SECONDARY OBJECITVES:

I. To determine safety and tolerability as determined by Common Terminology Criteria in Adverse Events (CTCAE) version 5.0 in each treatment arm.

II. To evaluate 9-month radiographic progression free survival in each arm as defined by Prostate Cancer Clinical Trials Working Group 3 (PCWG-3) for patients with bone metastases and RECIST version 1.1 for patients with measurable disease.

III. To evaluate radiographic progression free survival in each arm as defined by PCWG-3 for patients with bone metastases and RECIST version 1.1 for patients with measurable disease.

IV. To evaluate prostate-specific antigen (PSA) response defined as ≥ 50% decline in PSA from baseline using PCWG-3 criteria in patients in each treatment arm.

V. To evaluate time to PSA progression as defined by PCWG-3 criteria in patients in each treatment arm.

VI. To evaluate time to occurrence of first symptomatic skeletal event. VII. To evaluate time to first subsequent anti-cancer therapy (including androgen receptor signaling agents, cytotoxic chemotherapy, immunotherapy, or investigational agents) or death.

VIII. To evaluate overall survival, defined as time from registration to death due to any cause censored at the date of last follow-up, in each treatment arm.

IX. To evaluate patient-reported outcomes (PRO) via Patient-Reported Outcomes (PRO)-CTCAE in each treatment arm.

X. To evaluate duration of response as defined by RECIST version 1.1 for patients with measurable disease.

CORRELATIVE OBJECTIVES:

I. Correlate presence of molecular abnormalities with baseline clinical characteristics.

II. Evaluate co-occurring molecular alterations within each biomarker arm. III. Evaluate mechanisms of response and resistance using available tissue (archival or baseline) and circulating cell free tumor DNA (cfDNA) and circulating tumor cells (CTCs) at baseline, on treatment, and at progression.

IV. Evaluate efficacy parameters (objective response rate [ORR], PSA response, 9-month radiographic progression-free survival [rPFS], rPFS) based on arm allocation by:

IVa. DNA versus RNA qualifying molecular alterations; IVb. Blood versus tissue-based qualifying molecular alteration; IVc. Primary versus metastasis qualifying molecular alteration.

V. Evaluate efficacy parameters (ORR, PSA response, 9-month rPFS, rPFS) based on the following clinical parameters:

Va. Presence or absence of visceral metastases at baseline; Vb. Number of prior lines of therapy for metastatic castration resistant cancer (mCRPC) (one versus > 1); Vc. In patients having had prior exposure to taxane chemotherapy; Vd. Presence or absence of neuroendocrine differentiation at baseline. VI. Evaluate exceptional responders (defined as those with rPFS ≥ 18 months) and exceptional non-responders.

VII. To determine how circulating biomarker quantification correlates with clinical features and outcomes.

VIII. To determine the clinical impact of lineage plasticity alterations in predicting outcomes and response to therapy.

EXPLORATORY OBJECTIVE:

I. To compare patient-assessed adverse events via PRO-CTCAE™ with clinician-assessed adverse events in each treatment arm.

OUTLINE: Patients undergo genetic testing on previously-collected tissue samples. Patients are then assigned to 1 of 3 arms based on genetic testing results and Molecular Tumor Board (MTB) decision.

ARM A: Patients receive valemetostat tosylate orally (PO) once daily (QD) on days 1-28 of each cycle. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity.

ARM B: Patients receive carboplatin intravenously (IV) over 30 minutes and cabazitaxel IV over 60 minutes on day 1 of each cycle. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity.

ARM C: Patients receive one of the following treatment regimens per treating physician: 1) Cabazitaxel IV over 60 minutes on day 1 of each cycle. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. 2) Abiraterone acetate PO QD on days 1-28 of each cycle and prednisone PO twice daily (BID) on days 1-28 of each cycle. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. 3) Enzalutamide PO QD on days 1-28 of each cycle. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. 4) Lutetium Lu 177 vipivotide tetraxetan IV on day 1 of each cycle. Treatment repeats every 42 days for up to 6 cycles in the absence of disease progression or unacceptable toxicity.

All patients also undergo magnetic resonance imaging (MRI) or computed tomography (CT) and bone scan throughout the trial. Patients may also undergo optional fludeoxyglucose F-18 (FDG) or prostate-specific membrane antigen (PSMA) positron emission tomography (PET), as well as optional blood collection throughout the trial.

After completion of study treatment, patients without disease progression are followed every 2 months for the first 6 months and then every 3 months after that for up to 5 years. Patients with disease progression are followed every 6 months for 5 years.

Inclusion Criteria:

• PRE-REGISTRATION: Histological or cytological evidence of prostate cancer. Patients with variant histologies including neuroendocrine, small cell and sarcomatoid prostate cancer are allowed to enroll and these will not be used as selection criteria for individual arms. Central pathology review is not required.

• PRE-REGISTRATION: Measurable disease and/or non-measurable metastatic disease per RECIST version 1.1.

• PRE-REGISTRATION: Tissue procured within 12 months of pre-registration (metastatic disease preferred over primary tissue, though both are acceptable) available for submission per Section 6.2. For patients who have progressed on A032102 and are pre-registering again, repeat tissue procurement will not be mandated.

• PRE-REGISTRATION: Molecular report available performed as part of standard of care testing via any Clinical Laboratory Improvement Act (CLIA)-certified next generation sequencing (NGS) assay. Patients may be assigned based on pre-determined qualifying molecular/DNA alterations as stated in Section 4.8 after receipt of local molecular testing by the A032102 molecular tumor board (MTB). Final determination of arm assignment will be determined by the MTB. For qualifying DNA alteration determined by the MTB, testing may be from tumor tissue collected at any time or circulating tumor DNA (ctDNA) within 12 months of pre-registration. If no qualifying DNA alteration is identified based on the CLIA-certified next generation sequencing assay and MTB review, Caris testing, should be performed for both DNA/RNA profiling. Arm assignment based RNA requires testing of tumor tissue collected within 12 months of pre-registration and MTB review.

• PRE-REGISTRATION: Age ≥ 18 years.

• REGISTRATION: Progressive mCRPC as defined: 1) castrate levels of serum testosterone < 50 ng/dL AND one or more of the following criteria (choose all the apply):

  • PSA progression, defined by at least 2 consecutive rising PSA values at a minimum of 1-week intervals with the most recent PSA value being 2.0 ng/mL or higher, if confirmed PSA rise is the only indication of progression. Patients who received an anti-androgen must have PSA progression after withdrawal of anti-androgen therapy.
  • Radiographic progression per RECIST 1.1 criteria for soft tissue lesions
  • Bone metastasis progression per Prostate Cancer Working Group 3 (PCWG3) criteria.

• REGISTRATION: Patients selected to receive lutetium Lu 177 vipivotide tetraxetan treatment are required to have prostate-specific membrane antigen (PSMA) positive mCRPC as determined by investigator assessment. For reference, in the VISION trial this was defined as at least 1 PSMA+ metastatic lesion (defined as uptake greater than that of liver parenchyma in lesions of any size in any organ system) and no PSMA- lesions (defined as uptake equal to or lower than that of liver parenchyma in any lymph node with a short axis of at least 2.5 cm, in any solid organ lesion with a short axis of at least 1.0 cm, or in any bone lesion with a soft-tissue component of at least 1.0 cm in the short axis).

• REGISTRATION: Prior treatment with androgen receptor signaling inhibitor (ARSI) in either the metastatic hormone sensitive setting or mCRPC is required. Prior taxane therapy in either metastatic hormone sensitive setting or mCRPC is mandated unless patient is taxane ineligible or the patient refuses taxane therapy. Prior lutetium LU177 vipivotide tetraxetan treatment is permitted but not mandated. Patients with known germline or somatic deleterious BRCA 1/2 mutations must have received a prior PARPi.

• REGISTRATION: Resolved toxicities from previous anticancer therapy, defined as toxicities (other than alopecia) resolved to Common Terminology Criteria for Adverse Events (CTCAE) version 5.0, grade ≤ 1 or baseline. Note: Subjects may be enrolled with chronic, stable grade 2 toxicities (defined as no worsening to > grade 2 for at least 3 months prior to registration and managed with standard of care treatment) that the investigator deems related to previous anticancer therapy, comprised of:

  • Chemotherapy-induced neuropathy
  • Fatigue
  • Residual toxicities from prior treatment: Grade 1 or grade 2 endocrinopathies which may include: Hypothyroidism/hyperthyroidism. type I diabetes, hyperglycemia, adrenal insufficiency, adrenalitis, skin hypopigmentation (vitiligo)

• REGISTRATION: No cytotoxic, biologic, radiopharmaceutical or other non-kinase inhibitor investigational agent within 4 weeks of registration. Treatment with any type of small molecular kinase inhibitor (including investigational kinase inhibitor) within 2 weeks of registration. Treatment with abiraterone acetate, apalutamide, or darolutamide within 2 weeks of registration. Treatment with enzalutamide within 4 weeks of registration. No treatment with radiation therapy within 2 weeks of registration.

• REGISTRATION: No major surgery within 4 weeks of registration.

• REGISTRATION: No prior treatment with EZH inhibitors.

• REGISTRATION: Prior treatment with cabazitaxel + carboplatin.

• REGISTRATION: None of the following conditions:

  • Current use of moderate or strong cytochrome P450 (CYP)3A inducers.
  • Known or suspected hypersensitivity to valemetostat tosylate (DS-3201b) or any of the excipients.
  • For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load.

  * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial.

  • Imminent or established spinal cord compression based on clinical and/or imaging findings.
  • Known brain metastases or cranial epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks prior to registration after radiotherapy or at least 4 weeks prior to registration after major surgery (e.g., removal or biopsy of brain metastasis). Patients must have complete wound healing from major surgery or minor surgery before registration.
  • Significant cardiovascular defined as:
  • Myocardial infarction within 6 months prior to enrollment.
  • Uncontrolled angina pectoris within 6 months prior to enrollment.
  • New York Heart Association Class 3 or 4 congestive heart failure.
  • Corrected QT interval calculated by the Fridericia's formula (QTcF) ≥ 470 ms per electrocardiogram (ECG) within 42 days before randomization in any individual with any history of any cardiac disease or medication which can impact QTcF. Patients with known history or current symptoms of cardiac disease, history of treatment with cardiotoxic agents, or agents/conditions known to impact QTcF should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification and ECG.
  • Uncontrolled hypertension (resting systolic blood pressure >160 mmHg or diastolic blood pressure > 100 mmHg).
  • Clinically significant acute infection requiring systemic antibacterial, antifungal or antiviral therapy.
  • Moderate to severe hepatic impairment (Child-Pugh Class C)

• REGISTRATION: No freezing or donating sperm ≤ 14 days prior to registration.

• REGISTRATION: Eastern Cooperative Oncology Group (ECOG) performance status 0-2.

• REGISTRATION: No granulocyte colony-stimulating factor (GCSF) within 2 weeks of registration.

• REGISTRATION: No red blood cell (RBC) transfusions within 2 weeks of registration.

• REGISTRATION: No platelet transfusions within 2 weeks of registration.

• REGISTRATION: No bleeding diathesis.

• REGISTRATION: White blood cell count (WBC) ≥ 2,500/mcL.

• REGISTRATION: Absolute neutrophil count (ANC) ≥ 1,500/mcL.

• REGISTRATION: Hemoglobin ≥ 9 g/dL.

• REGISTRATION: Platelet count ≥ 100,000/mcL.

• REGISTRATION: Creatinine clearance ≥ 30 mL/min as defined by Cockcroft-Gault equation.

• REGISTRATION: Total bilirubin ≤ 1.5 x ULN (≤ 3 x upper limit of normal [ULN] for subjects with documented Gilbert's disease).

• REGISTRATION: Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3 x ULN.

• REGISTRATION: Albumin ≥ 2.8 g/dL.

• REGISTRATION: The A032102 molecular tumor board will review the local pathology report and molecular sequencing report, and the Alliance registration/randomization office will relay the assignment to the submitting site. Once the site receives this assignment, they can register the patient to A032102. Any questions about the molecular board treatment assignments can be directed to A032102@alliancenctn.org.

• RE-REGISTRATION: Progressive mCRPC (after receiving the tumor board assigned therapy) as defined: 1) castrate levels of serum testosterone < 50 ng/dL AND 2) progressive disease defined by radiographic progression on conventional imaging (CT/MRI chest, abdomen and pelvis and bone scan within 42 days of re-registration).

• RE-REGISTRATION: Resolved toxicities from previous anticancer therapy, defined as toxicities (other than alopecia) resolved to CTCAE version 5.0, grade ≤ 1 or baseline. Note: Subjects may be enrolled with chronic, stable grade 2 toxicities (defined as no worsening to > grade 2 for at least 3 months prior to registration and managed with standard of care treatment) that the investigator deems related to previous anticancer therapy, comprised of:

  • Chemotherapy-induced neuropathy
  • Fatigue
  • Residual toxicities from prior treatment: Grade 1 or grade 2 endocrinopathies which may include: Hypothyroidism/hyperthyroidism. type I diabetes, hyperglycemia, adrenal insufficiency, adrenalitis, skin hypopigmentation (vitiligo).

• RE-REGISTRATION: None of the following conditions:

  • Imminent or established spinal cord compression based on clinical and/or imaging findings.
  • Known brain metastases or cranial epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks prior to registration after radiotherapy or at least 4 weeks prior to re-registration after major surgery (e.g., removal or biopsy of brain metastasis). Patients must have complete wound healing from major surgery or minor surgery before re-registration.
  • Corrected QT interval calculated by the Fridericia's formula (QTcF) < 470 ms per ECG within 42 days before randomization in any individual with any history of any cardiac disease or medication which can impact QTcF.
  • Significant cardiovascular defined as:
  • Myocardial infarction within 6 months prior to enrollment.
  • Uncontrolled angina pectoris within 6 months prior to enrollment.
  • New York Heart Association Class 3 or 4 congestive heart failure.
  • Uncontrolled hypertension (resting systolic blood pressure > 160 mmHg or diastolic blood pressure > 100 mmHg).

• RE-REGISTRATION: ECOG Performance Status 0-2.

• RE-REGISTRATION: No GCSF within 2 weeks of registration.

• RE-REGISTRATION: No RBC transfusions within 2 weeks of registration.

• RE-REGISTRATION: No platelet transfusions within 2 weeks of registration.

• RE-REGISTRATION: WBC ≥ 2,500/mcL.

• RE-REGISTRATION: ANC ≥ 1,500/mcL.

• RE-REGISTRATION: Hemoglobin ≥ 9 g/dL (transfusions permitted).

• RE-REGISTRATION: Platelet count ≥ 100,000/mcL.

• RE-REGISTRATION: Creatinine clearance ≥ 30 mL/min as defined by Cockcroft-Gault equation.

• RE-REGISTRATION: Total bilirubin ≤ 1.5 x ULN (≤ 3 x ULN for subjects with documented Gilbert's disease).

• RE-REGISTRATION: AST and ALT ≤ 3 x ULN.

• RE-REGISTRATION: Albumin ≥ 2.8 g/dL.

• RE-REGISTRATION: QT Interval (QTcF) < 470 ms (in individuals with any cardiac history of any medication or condition known to impact QTcF).

• RE-REGISTRATION: The A032102 molecular tumor board will review the CARIS molecular sequencing report, the Alliance registration/randomization office will relay the assignment to the site. Any questions about the molecular board treatment assignments can be directed to A032102@alliancenctn.org.

Exclusion Criteria:

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