This study is an open-label, multicenter study designed to investigate the efficacy, safety and tolerability of FPI-2265 (225Ac-PSMA-I&T) in combination with Olaparib in participants with mCRPC. The dose optimization Phase 2 part will be investigating the safety, tolerability, and anti-tumor activity of novel dosing regimens of FPI-2265 and Olaparib in participants with metastatic castration-resistant prostate cancer.

This study is an open-label, multicenter study designed to investigate the efficacy, safety and tolerability of FPI-2265 (225Ac-PSMA-I&T) in combination with Olaparib in participants with mCRPC. The study will be conducted in two parts, with Part A enrolling participants who have been previously treated with lutetium-177 (177Lu) vipivotide tetraxetan or other 177Lu-PSMA radioligand therapy (RLT) and Part B enrolling participants who have not been previously treated with lutetium-177 (177Lu) vipivotide tetraxetan or other 177Lu-PSMA radioligand therapy. For each part of the study, a Simon 2-stage design will be used to evaluate two dosing regimens. The purpose of this investigation is to determine the recommended FPI-2265 dose and regimen. Conclusions from this Phase 2 study will be based on safety, tolerability, and anti-tumor activity data. Participants with PSMA-positive mCRPC will be allocated to Arm 1 and Arm 2 in a singular, alternating fashion, until all Stage 1 participants are enrolled into each of the two regimens:

Arm 1: Will consist of up to six doses of FPI-2265 every six weeks at Dose A and olaparib twice a day on days 1 to 14 of each cycle.

Arm 2: Will consist of up to nine doses of FPI-2265 every four weeks at Dose B and olaparib twice a day on days 1 to 14 of each cycle Participants will be monitored and assessed for efficacy response, disease progression, and adverse events.

Inclusion Criteria:

1. Adult male participants with mCRPC that is progressing at the time of study entry

2. ECOG performance status 0-1 and life expectancy of at least three months

3. Must have received at least one novel anti-androgen deprivation therapy

4. Participants with known BRCA mutations should have received approved therapies such as PARP inhibitors, per Investigator discretion.

5. All prior treatment-related AEs must have resolved to CTCAE Grade ≤1 (except alopecia).

6. Participants must have had prior orchiectomy and/or ongoing androgen deprivation therapy and a castrate level of serum testosterone (<50 ng/dL or <1.7 nmol/L)

7. Positive PSMA PET/CT scans .

8. Participants must have adequate organ and bone marrow function:

   • Hgb >/= 9g/dL
   • Platelets >/= 100 x 10^9/L
   • ANC </= 1.5 x 10^9/L
   • CrCL >/= 50 mL/min

Exclusion Criteria:

1. Previous treatment with any of the following within 6 months of first dose: Samarium-153, Rhenium-186, Rhenium-188, Radium-223, hemi-body irradiation.
2. Participants who received more than two (2) prior lines of cytotoxic chemotherapy for CRPC.
3. Participants with known unresolved urinary tract obstruction.
4. Transfusion- or growth factor-dependent participants.
5. Participants with a history of CNS metastases are excluded, except those who have received therapy (and are neurologically stable, asymptomatic, and not receiving corticosteroids for the purposes of maintaining neurologic integrity.
6. Symptomatic cord compression, or clinical or radiologic findings indicative of impending cord compression.
7. Participants with any liver metastases.
8. Participants with skeletal metastases presenting as a superscan .
9. Previous history of interstitial lung disease or non-infectious pneumonitis.
10. Participants with a history or clinical and/or laboratory features suggestive of MDS/AML.
11. Major surgery ≤28 days prior to the first dose of study treatment.
12. Planning to conceive a pregnancy during the treatment and up to six months after the last treatment.
13. Participants unable to swallow orally administered medications or with malabsorptive gastrointestinal disorders.
14. Concomitant use of known strong or moderate CYP3A inhibitors or inducers