Inclusion Criteria:

To be included in this study, participants should complete all screening procedures and meet all of the following criteria (i.e., evaluations performed as part of routine care prior to informed consent can be used for screening and eligibility confirmation):

• Willing and able to provide, or have a legally authorized representative provide, written informed consent and privacy authorization for the release of personal health information. A signed informed consent must be obtained before screening procedures are performed.

NOTE: Privacy authorization may be either included in the informed consent or obtained separately.

• 18 years of age and above

• Histological, pathological, and/or cytological confirmation of adenocarcinoma of the prostate.

• Prior orchiectomy and/or ongoing androgen-deprivation therapy and a castrate level of serum testosterone (<50 ng/dL or <1.7 nmol/L).

• Received ≥1 novel ARPI (e.g., enzalutamide, darolutamide, apalutamide and/or abiraterone).

• Eastern Cooperative Oncology Group (ECOG) status of 0-2 (Appendix A).

• Life expectancy of >6 months.

• Previously treated with, declined treatment with, or are considered unsuitable/unwilling for taxane regimen per investigator discretion.

• Prior completion of 2 cycles of lutetium 177 vipivotide tetraxetan between 16 and 6 weeks prior to initiation of study treatment, with evidence of PSA response between 0-90% decrease from the pre- lutetium 177 vipivotide tetraxetan baseline, documented by a PSA measurement obtained within 4 weeks of second dose of lutetium 177 vipivotide tetraxetan.

• Participants must have either:

  1. baseline measurable disease per RECIST v1.1 at time of screening or
  2. baseline PSA ≥ 2 ng/mL at time of screening.

• Patients must have adequate organ function:

  a. Bone marrow reserve: i. White blood cell (WBC) count ≥2.5 x 10⁹ /L OR absolute neutrophil count (ANC) ≥1.5 x 10⁹/L ii. Platelets ≥75 x 10⁹ /L iii. Hemoglobin ≥9 g/dL (9 g/dL is equivalent to 90 g/L and 5.59 mmol/L) b. Hepatic: iv. AST and ALT ≤ 3 X upper limit of normal (ULN) (or ≤ 5 X ULN for participants with liver involvement) v. total bilirubin (TBL) ≤ 1.5 X ULN (or ≤ 2 X ULN for participants with liver involvement). For patients with known Gilbert's Syndrome, < 3 X ULN is permitted.

  c. Renal: estimated glomerular filtration rate based on MDRD (Modification of Diet in Renal Disease) calculation ≥ 30 ml/min/1.73 m2.

  d. Pulmonary Function: Baseline oxygen saturation > 92% on room air at rest and no oxygen supplementation.

  e. Cardiac function: Left ventricular ejection fraction > 50% (screening echocardiography only required in subjects with known history of cardiac disease, prior MI, angina pectoris, coronary artery bypass graft (CABG), angioplasty, stent placement).

• Participants with partners of childbearing potential must agree to use a medically acceptable method of birth control (e.g., spermicide in conjunction with a barrier such as a condom) or sexual abstinence for the duration of the study including 6 months after the last dose of study drug. Sperm donation is prohibited during the study and for 6 months after the last dose of study drug. Female partners must use hormonal or barrier contraception unless postmenopausal or abstinent.

Exclusion Criteria:

• Any prior or concurrent malignancy whose natural history or treatment has the potential to interfere with the safety or efficacy assessments in the judgment of the site Principal Investigator (PI). Participants with prior history of malignancy that have been adequately treated and who have been disease-free for > 3 years are eligible, as are subjects with adequately treated non-melanoma skin cancer or superficial bladder cancer.
• Requirement for chronic systemic corticosteroid therapy (prednisone dose >10 mg per day or equivalent) or any other immunosuppressive therapies (including anti-TNFα therapies) unless stopped (with adequate tapering) within 7 days prior to dosing. Corticosteroid treatment for adverse event management as described in Section 6.1.10 is allowed.
• Previous PSMA-targeted radioligand therapy, aside from treatment with 2 cycles of lutetium 177 vipivotide tetraxetan, is not allowed.
• Prior PSMA radioligand therapy within 6 weeks of first dose of study treatment.
• Other concurrent cytotoxic chemotherapy, immunotherapy, radioligand therapy, PARP inhibitor, biological therapy, or investigational therapy.
• Untreated central nervous system metastases or leptomeningeal disease, symptomatic cord compression, or clinical or radiologic findings indicative of impending cord compression.
• Active systemic infection treated with IV antibiotics within 7 days prior to the first dose of study drugs.
• Active autoimmune disease that has required systemic treatment (except replacement therapy) within the past 2 years or any other diseases requiring immunosuppressive therapy while on study. Participants with Type I diabetes, vitiligo, psoriasis, hypo or hyperthyroid disease not requiring immunosuppressive treatment are permitted.
• History or evidence of inflammatory bowel disease (ulcerative colitis or Chron disease) or any other gastrointestinal disorder causing chronic nausea, vomiting or diarrhea (CTCAE ≥ grade 2).
• Evidence of interstitial lung disease or active, non-infectious pneumonitis, or uncontrolled asthma.
• Recent history of arterial (e.g. stroke or transient ischemic attack) or venous (e.g., pulmonary embolism or deep vein thrombosis) thrombosis; within 12 and 6 months prior to first dose of study treatment, respectively.
• Resting electrocardiogram (ECG) indicating uncontrolled, potentially reversible cardiac conditions, as determined by the investigator (e.g. unstable ischemia, uncontrolled symptomatic arrhythmia, congestive heart failure, corrected QT interval by Fredericia prolongation > 480 ms, electrolyte disturbances, etc), or patients with congenital long QT syndrome.
• Recent history of myocardial infarction and/or symptomatic congestive hear failure (New York Heart Association ≥ class II) within 12 months of first dose of study treatment, with the exception of ischemia or non ST segment elevation myocardial infarction controlled with stent placement and confirmed by a cardiologist more than 6 months prior to first dose of study treatment.
• Unresolved toxicities from prior anti-tumor therapy not having resolved to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 5.0 grade 1 or less, with the exception of alopecia, neuropathy, endocrinopathy, xerostomia, or toxicities that are stable and well-controlled.
• Known allergy to any of the compounds under investigation.
• Any other condition which, in the opinion of the investigator, would preclude participation in this trial.