A Study of TRC003 in the Treatment of Patients With Progressive PSMA-positive mCRPC

Inclusion Criteria: * Participants must have the ability to understand and sign ICF. * Participants must have histological, and/or cytological confirmation of adenocarcinoma of the prostate. * Participants must have progressive mCRPC after treatment of ARPI or taxane-based chemotherapy. * Participant must have been diagnosed with mCRPC with documented progressive disease. * Participants must have prior orchiectomy and/or ongoing androgen-deprivation therapy with a castrate level of serum testosterone (\< 50 ng/dL or \< 1.7 nmol/L). * Participants must have one or more PSMA-positive lesions whose PSMA uptake (SUVmax) is more than 2 fold of the blood pool. * Participants with an ECOG performance status of 0 - 2. * Participants must have adequate organ function * For participants who have partners of childbearing potential: Partner and/or patient must use a method of birth control with adequate barrier protection, deemed acceptable by the principal Investigator during the study and for 6 months after last investigational product administration. Exclusion Criteria: * Participants with mixed histology of prostate cancer (e.g., neuroendocrine). * Any FDG-positive and PSMA-negative target lesions. * Any investigational agents and other concurrent chemotherapy, targeted therapy, biologic agents, immunotherapy, radioligand therapy (androgen-deprivation therapy excepted) within 28 days or 5 half-lives prior to day of administration, whichever is longer. * Previous treatment with any conventional external beam radiotherapy including hemi-body radiation within 6 weeks before enrollment. * Previous bone-targeted therapy cannot be taken with a stable dose within 4 weeks before enrollment. * Known hypersensitivity to the components of the study therapy or its analogs. * Transfusion for the sole purpose of making a participant eligible for study inclusion within 28 days before administration. * A superscan as seen in the baseline bone scan. * Concurrent serious (as determined by the Investigator) medical conditions. * Diagnosed with other malignancies that are expected to alter life expectancy or may interfere with disease assessment.