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.