This phase II trial tests how well vorinostat works in treating patients with prostate-specific membrane antigen (PSMA)-low castration-resistant prostate cancer that has spread from where it first started (primary site) to other places in the body (metastatic) (mCRPC). Prostate cancer that has not spread to other parts of the body (localized) is typically treated through surgery or radiotherapy, which for many men is curable. Despite definitive local therapy, cancer that has come back after a period of improvement (recurrent) disease develops in 27-53% of men. Often this is detected by measurement of prostate-specific antigen (PSA) without visible evidence of metastatic disease. Lutetium Lu 177 vipivotide tetraxetan (177Lu-prostate specific membrane antigen [PSMA]-617) is a new small molecule PSMA-targeted radioactive therapy that has been approved by the Food and Drug Administration for the treatment of adult patients with PSMA-positive mCRPC who have been treated with androgen receptor inhibitors and taxane-based chemotherapy. Vorinostat is used to treat various types of cancer that does not get better, gets worse, or comes back during or after treatment with other drugs. Vorinostat is a drug which inhibits the enzyme histone deacetylase and may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving vorinostat and 177Lu-PSMA-617 may kill more tumor cells in in patients with PSMA-low mCRPC.

OUTLINE:

Patients receive vorinostat orally (PO) once a day (QD) for 28 days and then receive gallium Ga 68 gozetotide intravenously (IV) and undergo a positron emission tomography (PET) scan on trial. Patients may go on to receive 177Lu-PSMA-617 IV per standard of care (SOC) on day 1 of each cycle. Treatment repeats every 6 weeks for up to 6 cycles in the absence of disease progression or unacceptable toxicity. Patients undergo computed tomography (CT) and bone scan on trial and during follow-up, as well as a fludeoxyglucose F-18 (FDG) PET/CT during screening and on trial and single photon emission computed tomography (SPECT)/CT on trial. Patients undergo blood sample collection on trial and may also optionally undergo biopsy during screening and on trial.

After completion of study treatment, patients are followed up every 8 weeks for 6 months and then every 12 weeks for up to 2 years.

Inclusion Criteria:

• Documented histologically confirmed adenocarcinoma of the prostate.
• Patient must have evidence of castration resistant prostate cancer as evidenced by PSA progression (per Prostate Cancer Working Group 3 [PCWG3] criteria) and a castrate serum testosterone level (i.e., ≤ 50 mg/dL).
• PSMA SUVmean < 10 as determined by 68Ga-PSMA-11 PET.
• Patients must have received a next-generation androgen receptor-signaling inhibitor (e.g. abiraterone, enzalutamide, apalutamide, darolutamide). There must be at least a 2-week washout period after stopping these agents. Patients should be weaned off steroids at least 1 week prior to starting treatment.
• Eastern Cooperative Oncology Group (ECOG) performance status 0-2.
• At least one lesion (measurable and/or non-measurable) that can be accurately assessed at baseline by CT and/or bone scan and is suitable for repeated assessment.
• Hemoglobin ≥ 10 g/dL (measured within 28 days prior to administration of study treatment)
• Absolute neutrophil count (ANC) ≥ 1.5 x 10^9/L (measured within 28 days prior to administration of study treatment)
• Platelet count ≥ 100 x 10^9/L (measured within 28 days prior to administration of study treatment)
• Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (measured within 28 days prior to administration of study treatment)
• Aspartate aminotransferase (AST) and alanine transaminase (ALT) ≤ 2.5 x ULN, unless liver metastases are present in which case they must be ≤ 5 x ULN (measured within 28 days prior to administration of study treatment) . For patients with known Gilbert's Syndrome they must be ≤ 3 x ULN (measured within 28 days prior to administration of study treatment)
• Calculated creatinine clearance ≥ 50 mL/min (using Cockcroft-Gault formula) (measured within 28 days prior to administration of study treatment)
• Patients and their partners, who are sexually active and of childbearing potential must agree to the use of two highly effective forms of contraception in combination throughout the period of taking study treatment and for 3 months after last dose of study drug to prevent pregnancy in a partner.
• Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations.

Exclusion Criteria:

• Evidence of serious and/or unstable pre-existing medical, psychiatric or other condition that could interfere with patient safety or provision of informed consent to participate in this study.
• Evidence of metastatic neuroendocrine/small cell prostate cancer (NEPC). Note: baseline biopsy is not required but is strongly encouraged if a patient is found to have an FDG-positive/PSMA-negative lesion on baseline imaging.
• Patients receiving any systemic therapy (aside from an luteinizing hormone-releasing hormone [LHRH] analogue) or radiotherapy within 2 weeks prior to study treatment.
• Any previous treatment with an HDAC inhibitor (including valproic acid) or 177Lu-PSMA-617.
• Persistent toxicities (CTCAE grade >2) from prior cancer therapy, excluding alopecia and stable neuropathy.
• Patients considered a poor medical risk due to a serious, uncontrolled medical disorder or active, uncontrolled infection. Examples include, but are not limited to uncontrolled seizure disorder, unstable spinal cord compression, superior vena cava syndrome, or any psychiatric disorder that prohibits obtaining informed consent.
• Patients who are known to be serologically positive for human immunodeficiency virus (HIV) and a CD4 count < 200.
• Patients with known active hepatitis (i.e. Hepatitis B or C). Prior Hep C infection is allowed as long as polymerase chain reaction (PCR) is negative.
• Major surgery within 2 weeks of starting study treatment and patients must have recovered from any effects of any major surgery.
• Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication.
• Deep vein thrombosis or pulmonary embolism diagnosed within the past six months.
• Active use of coumarin-derived anticoagulant medication (i.e. warfarin).
• Serious cardiac disorder, including but not limited to uncontrolled ventricular arrhythmia, recent (within 12 months) myocardial infarction, resting electrocardiogram (ECG) indicating Fridericia's corrected QT interval prolongation > 500ms, or congenital long QT syndrome.