This is a three-part study evaluating the safety and efficacy of a PSMA-directed radioantibody (rosopatamab tetraxetan, conjugated to either In-111 or Ac-225). Part 1 will consist of one administration of In-111-rosopatamab tetraxetan to characterize the biodistribution of the radioantibody to target organs and prostate cancer lesions. Participants then will be enrolled into either Part 2 (Dose Optimization) or Part 3 (Dose Escalation and Expansion) depending on their prior treatment history. Participants qualifying for Part 2 will be randomized to receive Ac-225 rosopatamab tetraxetan in a single fractionated cycle (dose administration on Day 1 and Day 15) at either 45 or 60 kBq/Kg. Participants qualifying for Part 3 must have received prior Lu-177-PSMA-radioligand therapy and will receive Ac-225 rosopatamab tetraxetan in a single fractionated cycle at 45, 55, or 60 kBq/Kg. Dose limiting toxicities (DLTs) will be monitored in Part 3 to determine the recommended phase 2 dose (RP2D), and the study may enroll additional participants to be treated with the RP2D dose level. Participants enrolled into any part will attend study visits which will include blood samples, electrocardiogram (ECG), radiographic imaging, and physical examinations along with other assessments.

Inclusion Criteria:

• Progressive CRPC defined as castrate levels of testosterone and progressing by at least one of the following criteria:

  1. Serum PSA progression consisting of two consecutive increases in PSA measured at least 1 week apart. The minimal study baseline value is 2.0 ng/mL
  2. Soft tissue progression defined as a ≥20% increase in the sum of the diameter (short axis for nodal lesions and long axis for non-nodal lesions) of all target lesions based on the smallest sum of the diameter since the previous treatment was started or the appearance of one or more new lesions by CT/magnetic resonance imaging (MRI)
  3. Progression of bone disease defined by PCWG3 as evaluable disease or new bone lesions by bone scan
  4. Identification of new soft tissue or bone lesions on PSMA PET imaging

• Metastatic disease defined as either or both of the following:

  1. Parts 1, 2 and 3: Documented M1 disease on conventional imaging (CT/MRI of the chest/abdomen/pelvis and/or Technetium 99m [99mTc] whole-body bone scan)
  2. Parts 1 and 2 only: Identification of bone lesion(s), extra-pelvic soft tissue lesion(s), or visceral metastases on PSMA PET imaging with an FDA-approved imaging agent

• PSMA PET-positive disease, defined as at least one PSMA-positive metastatic lesion and no PSMA-negative lesions

• Progression following treatment with ADT and at least one ARSI (e.g., enzalutamide, apalutamide, darolutamide, and/or abiraterone acetate)

• The standard of care use (in the setting of metastatic CRPC with significant burden of active bone metastases) of antiresorptive bone-targeted agents (e.g., zoledronic acid, denosumab) is required for all participants without a contraindication, for at least 4 weeks prior to study drug administration

• Participants with HIV are eligible if they are well-controlled (i.e, an undetectable HIV viral load (<50 copies/mL) within 6 months of enrollment and a stable ART regimen for at least 6 months prior to enrollment) and at low risk for HIV-related illness

Part 3 Only:

• Prior treatment with Lu-177-PSMA-radioligand therapy
• Prior treatment with up to only one taxane-based chemotherapy regimen is allowed

Exclusion Criteria:

• Superscans by nuclear medicine/99mTc bone scan
• A known malignancy that is progressing or has required active treatment within the past 3 years other than CRPC, which is expected to alter life expectancy or may interfere with CRPC disease assessment
• Prior platinum-based chemotherapy
• Prior PARP inhibitors (e.g., olaparib or rucaparib)
• Prior treatment with Radium-223, Actinium-225, Strontium-89, Samarium-153, Rheunium-186, or Rhenium-188
• Participants receiving anti-coagulants or anti-platelet drugs (e.g., aspirin or nonsteroidal anti-inflammatory drugs [NSAIDs]) who cannot discontinue use if platelet count decreases to <50,000

Part 2 Only:

• Prior chemotherapy for CRPC. Prior taxane chemotherapy for HSPC is allowed if discontinued ≥1 year prior to randomization
• Prior radiopharmaceutical therapy (e.g., Ra-223, Lu-177-PSMA-617, or Lu-177-PSMA-I&T)
• Prior PSMA-targeted therapy

Part 3 Only:

• Prior PSMA-targeted therapy (e.g., antibody-drug conjugates or CAR-T therapy), except for Lu-177-PSMA-radioligand therapy