Can a second dose of this radioactive drug beat back prostate cancer again?

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Males ≥ 18 years of age * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 assessed within 7 days of study treatment initiation * Histologically or cytologically confirmed adenocarcinoma of prostate (Patients with small cell carcinoma of the prostate may be included) * Metastatic disease documented by at least one lesion on bone scan or abdominal/pelvic/chest computed tomography (CT) or magnetic resonance imaging (MRI) scan assessed by investigator. Patients without bone metastasis must have measurable lesions in extra-pelvic lymph nodes or in soft-tissues as defined by RECIST 1.1 criteria * Confirmed progression mCRPC despite ongoing androgen deprivation with serum testosterone \< 50ng/dl (1.7nM) within 3 months prior to screening. Progression is defined by the presence of at least one of the following criteria : * PSA progression using local laboratory values as defined by a minimum of 2 consecutive rising PSA levels with an interval of ≥1 week between each assessment where the PSA value at screening should be ≥1 ng/mL * Radiographic disease progression in bone based on PCWG3 criteria defined as the appearance of 2 or more new bone lesions on bone scan, with or without PSA progression * Radiographic disease progression in extra-pelvic lymph nodes based or soft-tissues on RECIST1.1 criteria with or without PSA progression * PSMA positive metastatic lesions on \[68Ga\]-PSMA-PET/CT without PSMA negative lesion (The presence of PSMA-positive lesions is defined as \[68Ga\]-PSMA-11 uptake greater than that of liver parenchyma in one or more metastatic lesions of any size in any organ system. The presence of PSMA-negative lesions is defined as PSMA 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 metastatic solid-organ lesions with a short axis of at least 1.0 cm, or in any metastatic bone lesion with a soft-tissue component of at least 1.0 cm in the short axis. Patients with any PSMA negative metastatic lesion meeting these criteria are ineligible). * Participants must have been previously treated with at least 4 consecutive cycles of \[177Lu\]Lu-PSMA with no evidence of progression during this first course of treatment (including radiological, clinical but also PSA progression). * Participants must have been previously treated with at least one ARSI - Androgen Receptor Signaling Inhibitors - (including enzalutamide, apalutamide, abiraterone or darolutamide) initiated for mCSPC, nmCRPC or mCRPC. (ARSI may be also administered together with \[177Lu\]Lu-PSMA-617 provided that the patient has not received an identical ARSI in the past and that this ARSI was initiated at least 15 days before the first cycle of \[177Lu\]Lu-PSMA-617 and less than 2 months ago. The ARSI administrated in association with LuPSMA should not be considered as a prior therapy. A previous ARSI treatment is mandatory for patient eligibility) * Patients must have been previously treated with at least one taxane based chemotherapy (with docetaxel or cabazitaxel) (The number of previously administrated lines of taxane-based therapy is not limited ; patients can have received a taxane-based chemotherapy before or after the first sequence of \[177Lu\]Lu-PSMA) * Patients must have been progressed at least 120 days after the last injection of the first course of \[177Lu\]Lu-PSMA therapy. (Patients with a radiological or clinical progressive disease during the first 120 days after the last cycle of the first course of \[177Lu\]Lu-PSMA are not eligible. PSA progression is defined by a ≥ 25% increase in PSA and an absolute increase of 2 ng/mL or more from the NADIR and confirmed by a second consecutive value obtained 3 or more weeks later. Patients treated with chemotherapy, ARSI or PARP inhibitors between the first 117LuPSMA course and screening are also eligible). * Be abstinent from heterosexual intercourse OR must agree to use contraception unless confirmed to be azoospermic (vasectomized or secondary medical cause) until 98 days (14 weeks) post-treatment. * Adequate organ functions : * Bone marrow reserve : * ANC ≥ 1.5 X 109/L * Platelets ≥ 100 X 109/L * Hemoglobin ≥ 10 g/dL * Hepatic : * Total bilirubin ≤ 2 x ULN. For patients with known Gilbert's syndrome ≤ 3 x ULN. * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) ≤3 x ULN * Renal : * Clearance ≥40 ml/mn * Patients must have signed informed consent prior to participating in any study related procedures * Willing and able to comply with the protocol, including follow-up visits and examinations * Patients have to be affiliated to the French social security system, or equivalent Exclusion Criteria: * History of a \[177Lu\]Lu-PSMA serious adverse event (SAE) or CTCAE Grade 3 or 4 AE during the initial course of \[177Lu\]Lu-PSMA that led to the discontinuation of treatment * More than one course of \[177Lu\]Lu-PSMA therapy * Less than 120 days from the last dose administrated in the initial course of \[177Lu\]Lu-PSMA treatment and the radiological or clinical disease progression, or the initiation of a subsequent therapy. * Any history of treatment with radium-223 dichloride or other systemic radiotherapy (including strontium-89, samarium-153, actinium-PSMA...) * Transfusion of red blood cells within 30 days prior to the first injection of the re-treatment of \[177Lu\]Lu-PSMA-617 * Current central nervous system (CNS) metastases * Hypersensitivity to the active substance (Lutetium \[177Lu\] vipivotide tetraxetan or Gallium \[68Ga\] gozetotide) or to any of the excipients * Prior \> hemibody external radiotherapy * Imminent or established spinal cord compression based on clinical findings and / or MRI that has not yet been treated * Other malignancy treated within the last 3 years (except non-melanoma skin cancer or low-grade superficial bladder cancer) * Chronic conditions associated with non-malignant abnormal bone growth (e.g., confirmed Paget's disease of bone) * Ongoing participation in any other clinical trial who may interfere with the present study in the judgment of the investigator * Concurrent serious (as determined by the Principal Investigator) medical conditions, including, but not limited to, uncontrolled infection, known active hepatitis B or C, or other significant co-morbid conditions that in the opinion of the investigator would impair study participation or cooperation. * Active clinically significant cardiac disease * History of somatic or psychiatric disease/condition that may interfere with the objectives and assessments of the study * Patients under tutorship or guardianship