The Present Study Aims to Compare Patients Who Receive the Investigational Product (177Lu-DOTA-rosopatamab) Plus Standard of Care, in Comparison to Standard of Care Only

Inclusion Criteria:

1. Be a male, at least 18 years old, with metastatic adenocarcinoma of the prostate defined by histological / pathological confirmation of PC.
2. Be of ECOG Performance Status 0, 1, or 2 and have an estimated life expectancy of ≥6 months.
3. Have metastatic disease (≥1 metastatic lesions present on baseline CT, MRI, or bone scan imaging).
4. Have castration-resistant PC (defined as disease progressing despite castration by orchiectomy or ongoing use of luteinizing hormone-releasing hormone \[LHRH\]) and must have a castrate level of serum/plasma testosterone (\<50 ng/dL or \<1.7 nmol/L).
5. In the mCRPC setting, must have received a minimum of 12 weeks of prior therapy with a NAAD, either enzalutamide or abiraterone plus prednisone.
6. Should have received one line of prior taxane therapy or have refused or be ineligible for taxanes
7. Have a disease that is progressing at study entry, despite a castrate testosterone level (\<50 ng/dL or \<1.7 nmol/L), by the demonstration of at least one of the following:

   1. Rising PSA values done in sequence at least 1 week apart and with a minimal starting value of 2.0 ng/mL.
   2. Progressive disease or new lesion(s) in the viscera or lymph nodes as per RECIST1.1 or in bone as per Prostate Cancer Working Group 3 \[PCWG3; Scher et al., 2016\]). Any ambiguous results are to be confirmed by other imaging modality (e.g., CT or MRI scan).
8. Have disease that is PSMA positive, as demonstrated by a 68Ga-PSMA11 PET/CT scan and confirmed as eligible by the Sponsor's central reader (patient must have at least one site of metastatic disease with SUVmax ≥1.5 times the SUV of normal liver). If the disease meets the criteria for PSMA positivity, but there is one or more soft tissue lesion of ≥ 2 cm that is not PSMA positive, then the patient is to be excluded on the grounds that there is substantial disease which might not respond to the therapy.
9. Must have recovered to ≤ Grade 2 from all clinically significant toxicities related to prior therapies (i.e., surgery, local radiotherapy, NAAD, chemotherapy, etc.).
10. Can be receiving a bisphosphonate or denosumab regimen provided that the patient has been receiving and tolerating this treatment for ≥30 days prior to randomization.
11. Have adequate organ function at Screening:

    a. Bone marrow: i. Platelets ≥150×109/L. ii. Absolute neutrophil count \>1.5×109/L. iii. Hemoglobin ≥10g/dL (no red blood cell transfusion in the previous 4 weeks).

    b. Liver function: i. Total bilirubin \< 1.5×the upper limit of normal (ULN). For patients with known Gilbert's Syndrome \<3×ULN is permitted. ii. Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) \<3×ULN OR \<5×ULN for patients with liver metastases. c. Renal function: i. Serum/plasma creatinine \<1.5×ULN or creatinine clearance ≥50 mL/min determined using the Cockcroft \& Gault formula.
12. Have the capacity to understand the study and be able and willing to comply with all protocol requirements.
13. Patients must comply with the radiation protection rules (including hospital admissions and isolation) that are used by the treating institution in order to protect their contacts and the general public, especially if a female partner of the patient is or could be pregnant.
14. Must agree to practice adequate precautions to prevent pregnancy in a partner and to avoid potential problems associated with radiation exposure to the unborn child (Refer to Clinical Trials Facilitation Group, 2020: Recommendations related to contraception and pregnancy testing in clinical trials Version 1.1, CTFG, 2020).

Exclusion Criteria:

1. Are unable to understand or are unwilling to sign a written informed consent document or to follow investigational procedures in the opinion of the Investigator.
2. Have PC associated with pathological findings consistent with small cell or any histology other than adenocarcinoma of the prostate. If there are minor elements of neuroendocrine histology, this is acceptable.
3. Uncontrolled pain.
4. Diagnosed with other malignancies that are expected to alter life expectancy or may interfere with disease assessment. However, patients with a prior history of malignancy that has been adequately treated and who have been disease-free for more than 3 years are eligible, as are patients with adequately treated non-melanoma skin cancer, and superficial bladder cancer.
5. Are at increased risk of hemorrhage or bleeding, or with a recent history of a thrombolytic event (e.g., deep vein thrombosis \[DVT\]/ pulmonary embolism \[PE\]) and have been administered long-term anti-coagulant or anti-platelet agents.
6. Have received prior treatment with monoclonal antibody (mAb) J591 or HuJ591 or any other PSMA targeted therapy.
7. Have known allergies, hypersensitivity, or intolerance to the investigational drug or its excipients.
8. Have received prior systemic anti-cancer therapy (e.g., chemotherapy, immunotherapy, or biological therapy) and/or radiation therapy within 4 weeks of randomization OR if any significant AEs have not resolved to National Cancer Institute (NCI) AE Criteria ≤2; OR are receiving other concurrent cytotoxic chemotherapy, immunotherapy, radioligand therapy, or investigational therapy.
9. Have received prior treatment with radioisotopes, including but not limited to: 89Strontium, 153Samarium, 186Rhenium, 188Rhenium, 223Radium, or hemi-body irradiation within 6 months prior to randomization.
10. Have received other investigational therapy within 4 weeks of randomization.
11. Have known brain metastases or hepatic metastases.
12. Have a history of seizure and/or stroke within past 6 months.
13. Have clinical or radiologic findings indicative of impending cord compression or experience symptomatic cord compression.
14. Have a serious active or sub-clinical infection or angina pectoris (New York Heart Association \[NYHA\] Class III or IV), significantly prolonged QT interval or other serious illness(es) involving the cardiac, respiratory, central nervous system, renal, hepatic or hematological organ systems, which might impair the ability to complete this study or could interfere with determination of causality of any adverse effects experienced in this study, or which require treatment that could interact with study treatment, particularly with enzalutamide.
15. Have received treatment with any PARP inhibitors (i.e., Olaparib) or with any platinum based anti-neoplastic drugs.
16. Have a known alteration in breast cancer genes (BRCA) BRCA1, BRCA2, or Ataxia Telangiectasia Mutated Gene (ATM) gene and are eligible to receive Olaparib therapy according to their institution's SoC