Key Inclusion Criteria:

* Male and ≥18 years at the time of providing written informed consent.
* Histologically confirmed prostate adenocarcinoma.
* For subjects who have not undergone an orchiectomy, must be undergoing treatment with a luteinizing hormone-releasing hormone (LHRH) agonist or antagonist and must agree to continue such therapy while on study treatment. Subjects enrolled to mCRPC cohorts must have serum testosterone levels of ≤50ng/dL (1.73nM at Screening).
* Must receive prior treatment(s) as defined in the protocol for each cohort
* Documented evidence of disease progression on or after the most-recent prior regimen for mCRPC cohorts
* mCSPC combination cohorts: High volume metastatic disease documented by CT/MRI and/or 99mTC bone scan (for bone lesions)
* Adequate blood counts
* Must have at least 1 PSMA-positive metastatic lesion and no measurable PSMA-negative lesions by local assessment for alternative dosing regimen and combination cohorts.

Key Exclusion Criteria

* Receipt of chemotherapy within 21 days prior to enrollment; hormonal therapy (not including LHRH analogs) within 7 days prior to enrollment; palliative radiation therapy within 7 days prior to enrollment; or any other anticancer therapy within 21 days prior to enrollment or other therapy for monotherapy cohorts
* Receipt of more than 1 prior taxane regimen or non-taxane chemotherapy for prostate cancer for alternative dose regimen and mCRPC combination cohorts
* Receipt prior apalutamide, enzalutamide, or darolutamide, or AAP for mCRPC combination cohorts
* Receipt any prior chemotherapy or prior ARPI, and must be greater than 90 days of ADT prior to enrollment for mCSPC combination cohorts
* Use of chronic systemic glucocorticoids equivalent to > 10 mg prednisone daily. Note: short-term administration of systemic corticosteroids > 10 mg prednisone equivalent (e.g., for allergic reactions or management of immune- or infusion-related AEs) is allowed.
* Symptomatic and/or untreated central nervous system (CNS) metastases. Patients with asymptomatic, untreated CNS metastases are eligible provided they have been clinically stable (neurologically stable and not requiring steroids for at least 28 days prior to enrollment).
* History of any invasive malignancy (other than primary) within the previous 2 years prior to the enrollment date that requires active therapy or is at high risk of recurrence in the opinion of the investigator.
* Marked baseline prolongation of QT/QT interval corrected for heart rate (QTc), e.g., a triplicate-average QTc interval > 480 milliseconds (CTCAE Grade 2) using Fridericia's QT correction formula at any time within 28 days before enrollment, ongoing history of CTCAE Grade ≥2 QTc at enrollment, or anticipated need to perform repeat ECG evaluations to satisfy re-treatment criteria.
* Prior history of interstitial lung disease, pneumonitis, or other clinically significant lung disease within 12 months prior to enrollment date.
* Clinically significant ocular findings by a qualified ophthalmologist or optometrist including active ocular infections or chronic corneal disorders unless approved by the Medical Monitor.
* Peripheral neuropathy Grade ≥ 2 within 28 days prior to enrollment.
* For combination cohorts with apalutamide: no prior history of seizure or condition that may predispose to seizure (including but not limited to prior cerebrovascular accident, TIA or loss of consciousness within the last 12 months, brain AVM, brain metastases).
* 24-hour urine protein > 1g/24h