Safety and Efficacy of Therapies for Metastatic Castration-resistant Prostate Cancer (mCRPC)

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 Acapatamab (or AMG 404 in Part 3) * No acute symptoms of COVID-19 disease within 10 days prior to first dose of Acapatamab (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 Subprotocol D only: Inclusion criteria * Subjects may have had novel hormonal therapies (NHT; eg, abiraterone, enzalutamide, apalutamide, or darolutamide) for prostate cancer, but no more than 1 NHT for metastatic prostate cancer * Ineligible for or refuse taxane therapy