All parts

        Inclusion Criteria:

          -  ≥ 18 years of age (or legal adult age within country)

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

          -  Subjects with mCRPC with histologically or cytologically confirmed adenocarcinoma of
             the prostate

          -  Subjects should have undergone bilateral orchiectomy or should be on continuous
             androgen deprivation therapy with a gonadotropin releasing hormone agonist or
             antagonist (testosterone ≤ 50 ng/dL (or 1.7 nmol/L))

        Exclusion Criteria:

          -  Central nervous system (CNS) metastases or leptomeningeal disease

          -  History or presence of clinically relevant CNS pathology

          -  Confirmed history or current autoimmune disease or other diseases requiring permanent
             immunosuppressive therapy

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

          -  Prior treatment with a taxane for mCRPC

          -  Major surgery and/or Radiation within 4 weeks

          -  History or evidence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)
             infection unless agreed upon with medical monitor and meeting the following criteria:

               -  Negative test for SARS-CoV-2 RNA by real time polymerase chain reaction (RT-PCR)
                  within 72 hours of first dose of AMG 160 (or AMG 404 in Part 3)

               -  No acute symptoms of COVID-19 disease within 10 days prior to first dose of AMG
                  160 (or AMG 404 in Part 3) (counted from day of positive test for asymptomatic
                  subjects)

        Prior/Concurrent Clinical Study Experience

          -  Currently receiving treatment in another investigational device or drug study, or less
             than 4 weeks since ending treatment on another investigational device or drug
             study(ies). Other investigational procedures while participating in this study are
             excluded with the exception of investigational scans.

        Subprotocol A only:

        Inclusion criteria

        • Subjects planning to receive enzalutamide for the first time for mCRPC

        Exclusion criteria

          -  Use of strong CYP2C8 inhibitors or strong CYP3A4 inducers

          -  Use of narrow therapeutic index drugs that are substrates of CYP3A4, CYP2C9 or CYP2C19

        Subprotocol B only:

        Inclusion criteria

          -  Subjects planning to receive abiraterone for the first time for mCRPC Exclusion
             criteria

          -  Baseline moderate and severe hepatic impairment (Child-Pugh Class B and C)

          -  Presence of uncontrolled hypertension, hypokalemia, or fluid retention

          -  History or presence of adrenocortical insufficiency

          -  Use of concomitant medications that are sensitive substrates for CYP2D6 with a narrow
             therapeutic index

          -  Use of strong CYP3A4 inducers

        Subprotocol C only:

        Inclusion criteria

          -  Subjects who are refractory to a novel antiandrogen therapy. Subjects must be
             ineligible for or refuse taxane therapy.

          -  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 Exclusion criteria

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

          -  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 dose