Phase I Study of 225Ac-J591 Plus 177Lu-PSMA Small Molecule for Progressive Metastatic Castration Resistant Prostate Cancer

Inclusion Criteria: * Histologically or cytologically confirmed adenocarcinoma of prostate * Documented progressive metastatic CRPC based on Prostate Cancer Working Group 3 (PCWG3) criteria, which includes at least one of the following criteria: PSA progression, Objective radiographic progression in soft tissue, New bone lesions * ECOG performance status of 0-2 * Have serum testosterone \< 50 ng/dL. Subjects must continue primary androgen deprivation with an LHRH/GnRH analogue (agonist/antagonist) if they have not undergone bilateral orchiectomy * Have previously been treated with at least one of the following: Androgen receptor signaling inhibitor (such as enzalutamide), CYP 17 inhibitor (such as abiraterone acetate) * Have previously received taxane chemotherapy, been determined to be ineligible for taxane chemotherapy by their physician or refused taxane chemotherapy * Age \> 18 years * Patients must have normal organ and marrow function as defined below: Absolute neutrophil count: \>2,000 cells/mm3, Hemoglobin: ≥9 g/dL, Platelet count: \>150,000 x 109/uL, Serum creatinine: \<1.5 x upper limit of normal (ULN) or calculated creatinine clearance ≥ 60 mL/min/1.73 m2 by Cockcroft-Gault, Serum total bilirubin: \<1.5 x ULN (unless due to Gilbert's syndrome in which case direct bilirubin must be normal), Serum AST and ALT: \<1.5 x ULN in the absence of liver metastases; \<3 x ULN if due to liver metastases (in both circumstances bilirubin must meet entry criteria) * Ability to understand, and the willingness to sign, a written informed consent document Exclusion Criteria: * Implantation of investigational medical device ≤4 weeks of Treatment visit #1 (Day 1) or current enrollment in oncologic investigational drug or device study * Use of investigational drugs ≤4 weeks or \<5 half-lives of Treatment visit # 1(Day 1) or current enrollment in investigational oncology drug or device study * Prior systemic beta-emitting bone-seeking radioisotopes. Prior radium-223 is allowed provided at least 90 days have lapsed since last dose * For the prior PSMA-TRT-naive cohort, prior PSMA-targeted radionuclide therapy is not allowed (prior PSMA-targeted isotopes used for imaging/diagnostic purposes are allowed, as is prior PSMA-targeted therapy that does not involve therapeutic radionuclides); For the 177Lu-PSMA small molecule exposed cohort, no dose limiting toxicity may have been observed during/after therapy with prior treatment and all other entry criteria must be met * Known active brain or leptomeningeal metastases * History of deep vein thrombosis and/or pulmonary embolus within 1 month of Treatment visit #1 * Other serious illness(es) involving the cardiac, respiratory, CNS, renal, hepatic or hematological organ systems which might preclude completion of this study or interfere with determination of causality of any adverse effects experienced in this study * Radiation therapy for treatment of PC ≤4 weeks of Treatment visit #1 * Patients on stable dose of bisphosphonates or denosumab, which have been started no less than 4 weeks prior to treatment start, may continue on this medication, however patients are not allowed to initiate bisphosphonate/Denosumab therapy during the DLT-assessment period of the study * Having partners of childbearing potential and not willing to use a method of birth control deemed acceptable by the principle investigator and chairperson during the study and for at least 140 days after last study drug administration * Currently active other malignancy other than non-melanoma skin cancer. Patients are considered not to have "currently active" malignancy if they have completed any necessary therapy and are considered by their physician to be at less than 30% risk of relapse * Known history of myelodysplastic syndrome * Bone scan with confluent lesions and lack of urinary tracer consistent with a "superscan" as determined by the investigator * Prior exposure to PARP inhibitor \> 2 weeks