All Parts

        Inclusion Criteria:

          -  Subject has provided informed consent prior to initiation of any study-specific
             activities/procedures

          -  Subjects with histologically or cytologically confirmed mCRPC who are refractory to a
             novel antiandrogen therapy (abiraterone, enzalutamide, and/or apalutamide) and have
             failed at least 1 (but not more than 2) taxane regimens (or who are deemed medically
             unsuitable to be treated with a taxane regimen or have actively refused treatment with
             a taxane regimen). Progression on novel antiandrogen therapy may have occurred in the
             non-metastatic CRPC setting

          -  Subject should have undergone bilateral orchiectomy or should be on continuous
             androgen-deprivation therapy (ADT) with a gonadotropin-releasing hormone (GnRH)
             agonist or antagonist

          -  Total serum testosterone </= 50 ng/dL or 1.7 nmol/L

          -  Evidence of progressive disease, defined as 1 or more PCWG3 criteria:

        PSA level >/=1 ng/mL that has increased on at least 2 successive occasions at least 1 week
        apart, nodal or visceral progression as defined by RECIST 1.1 with PCGW3 modifications,
        and/or appearance of 2 or more new lesions in bone scan

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 - 1

          -  Life expectancy >/=6 months

        Exclusion Criteria:

          -  Any anticancer therapy or immunotherapy within 4 weeks of start of first dose, not
             including luteinizing hormone-releasing hormone agonist (LHRH)/GnRH analogue
             (agonist/antagonist). Subjects on a stable bisophosphonate or denosumab regimen for
             >/= 30 days prior to randomization are eligible

          -  Prior PSMA-targeted therapy (subjects on prior therapy may be eligible if discussed
             with Amgen medical monitor prior to enrollment)

          -  Central nervous system (CNS) metastases, leptomeningeal disease, or spinal cord
             compression

          -  Active autoimmune disease or any other diseases requiring immunosuppressive therapy
             while on study

          -  Needing chronic systemic corticosteroid therapy (prednisone > 10 mg per day or
             equivalent) or any other immunosuppressive therapies (including anti-tumor necrosis
             factor alpha [TNF alpha] therapies) unless stopped 7 days prior to start of first dose

          -  Myocardial infarction, unstable angina, cardiac arrhythmia requiring medication,
             and/or symptomatic congestive heart failure (New York Heart Association > class II)
             within 12 months of first dose of AMG 160

        Part 2 only:

          -  Subjects on a prior PD-1 or PD-L1 inhibitor who experienced a Grade 3 or higher
             immune-related adverse event prior to first day of dosing

          -  History or evidence of interstitial lung disease or active, non-infectious pneumonitis

        Part 3 only:

        -Evidence of active tuberculosis on chest radiograph within 3 months prior to the first
        dose of investigational product

        Part 6 only:

        Subjects are excluded from this cohort if any of the following additional criteria apply:

          -  Subjects taking strong OAT3 inhibitors (eg, probenecid) or adjust the dosing to 1 mg
             PO QD.

          -  Subjects with latent or active tuberculosis at screening