The purpose of this study is to evaluate the change in the expression of treatment targets on the surface of tumor cells (Prostate Specific Membrane Antigen (PSMA), Somatostatin Receptor 2 (SSTR2), and Gastrin Releasing Peptide Receptor (GRPR) between the baseline and following targeted radioligand therapy (RLT). Study will use radioligand imaging (RLI) to determine predominantly expressed target on the surface of tumor cells. Based on predominant expression of target, corresponding RLT targeting PSMA, SSTR2, or GRPR RLT will be given for up to 6 cycles every 6 weeks as intravenous (i.v.) injection in participants with metastatic neuroendocrine prostate cancer (mNEPC). Study is planning to enroll approximately 20 participants in \[177Lu\]Lu-PSMA-617 treatment arm, approximately 3 participants in \[177Lu\]Lu-NeoB treatment arm, and approximately 13 participants in \[177Lu\]Lu-DOTA-TATE treatment arm.

The screening period for each participant includes imaging with 3 radioligand imaging (RLI) compounds to assess expression level of PSMA, SSTR2 and GRPR. Participants will be assigned to the radioligand treatment (RLT) corresponding to their predominantly expressed target based on blinded independent central review (BICR). During the treatment period, participants will receive up to 6 cycles of the assigned RLT, corresponding to a total dose of 44.4 GBq (+/-10%) for \[177Lu\]Lu-PSMA-617 or \[177Lu\]Lu-DOTA-TATE , and 55.5 GBq (+/-10%) for \[177Lu\]Lu-NeoB. No crossover to a different type of RLT is allowed. At least six weeks after receiving the first cycle of RLT, participants must be scanned again with up to 3 RLIs but must be scanned, with at least with one RLI corresponding to the received RLT, which is recommended to be performed first. All post-baseline PET/CT scans should be performed using the same PET/CT imaging agent and same PET/CT camera, acquisition and reconstruction protocols as used for screening PET/CT for the participant. The post-treatment follow-up period consists of a 42-days post EOT safety follow-up visit, efficacy, and survival follow-up until radiographic disease progression, death, lost to follow-up or withdrawal of consent, whichever occurs first. The planned duration of treatment is up to 36 weeks for all treatment arms in this study, with treatment given every 6 weeks ±7 days. Participants may be discontinued from treatment earlier due to unacceptable toxicity or disease progression, and/or at the discretion of the Investigator or the participant.