Inclusion Criteria:

• Subject has provided informed consent/assent prior to initiation of any study specific activities/procedures.
• Age is greater than or equal to 18 years
• Subjects with histologically or cytologically confirmed mCRPC who are refractory to a novel antiandrogen therapy (eg, abiraterone and/or enzalutamide)) 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).
• Dose escalation: novel antiandrogen therapy must have been given for treatment of metastatic disease
• Dose expansion: progression on novel antiandrogen therapy may have occurred in the non-metastatic or metastatic setting
• Subjects must have undergone bilateral orchiectomy or be on continuous ADT with a gonadotropin releasing hormone (GnRH) agonist or antagonist
• Total serum testosterone is less than or equal to 50 ng/dL or 1.7 nmol/L
• Evidence of progressive disease, defined as 1 or more PCWG3 criteria:
• PSA level is greater than or equal to 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
• appearance of 2 or more new lesions in bone scan
• Eastern Cooperative Oncology Group (ECOG) performance status of 0-1
• Life expectancy greater than or equal to 3 months
• Adequate organ function, defined as follows:

Hematological function:

• absolute neutrophil count is greater than or equal to 1 x 109/L (without growth factor support within 7 days from screening assessment)
• platelet count is greater than or equal to 75 x 109/L (without platelet transfusion within 7 days from screening assessment)
• hemoglobin is greater than or equal to 9 g/dL (90 g/L) (without blood transfusion within 7 days from screening assessment)

Renal function:

• estimated glomerular filtration rate based on MDRD (Modification of Diet in Renal Disease) calculation is greater than or equal to 30 ml/min/1.73 m2

Hepatic function:

• aspartate aminotransferase (AST) and alanine aminotransferase (ALT) is less than 3 x ULN (or less than 5 x ULN for subjects with liver involvement)
• total bilirubin (TBL) is less than 1.5 x ULN (or is less than 2 x ULN for subjects with liver metastases)

Cardiac function:

• left ventricular ejection fraction is greater than 50% (2-D transthoracic echocardiogram [ECHO] is the preferred method of evaluation; multi gated acquisition scan is acceptable if ECHO is not available)
• baseline ECG QTcF is less than 470 msec

Exclusion Criteria:

Disease Related

• Pathological finding consistent with pure small cell, neuroendocrine carcinoma of the prostate or any other histology different from adenocarcinoma
• Radiation therapy within 4 weeks of first dose (or local or focal radiotherapy within 2 weeks of first dose)
• Untreated central nervous system (CNS) metastases or leptomeningeal disease. Patients with a history of treated CNS metastases are eligible if there is radiographic evidence of improvement upon the completion of CNS-directed therapy and no evidence of interim progression between the completion of CNS directed therapy and the screening radiographic study.

Other Medical Conditions

• Prior major surgery within 4 weeks of first dose
• Confirmed history or current autoimmune disease or other diseases resulting in permanent immunosuppression or requiring permanent immunosuppressive therapy
• Presence of fungal, bacterial, viral, or other infection requiring IV antimicrobials for management within 7 days of dosing NOTE: Simple urinary tract infections and uncomplicated bacterial pharyngitis are permitted if responding to active treatment and after consultation with sponsor. Screening for chronic infectious conditions is not required
• Positive test for human immunodeficiency virus (HIV)
• Exclusion of hepatitis infection based on the following results and/or criteria:
• Positive for hepatitis B surface antigen (HBsAg) (indicative of chronic hepatitis B or recent acute hepatitis B).
• Negative HBsAg and positive for hepatitis B core antibody: Hepatitis B virus DNA by polymerase chain reaction (PCR) is necessary. Detectable hepatitis B virus DNA suggests occult hepatitis B.
• Positive Hepatitis C virus antibody (HCVAb): hepatitis C virus RNA by PCR is necessary. Detectable hepatitis C virus RNA suggests chronic hepatitis C.
• History of arterial or venous thrombosis (eg, stroke, transient ischemic attack, pulmonary embolism, or deep vein thrombosis) within 12 months of first dose of AMG 509
• Myocardial infarction and/or symptomatic congestive heart failure (New York Heart Association > class II) within 12 months of first dose of AMG 509
• Unresolved toxicities from prior anti-tumor therapy not having resolved to Common Terminology Criteria for Adverse Events (CTCAE) version 5.0 grade 1, with the exception of alopecia or toxicities that are stable and well-controlled AND there is agreement to allow by both the investigator and sponsor
• History of other malignancy within the past 2 years, with the following exception(s):
• malignancy treated with curative intent and with no known active disease present for greater than or equal to 1 years before enrollment and felt to be at low risk for recurrence by the treating physician
• adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease
• adequately treated urothelial papillary noninvasive carcinoma or carcinoma in situ
• History or evidence of inflammatory bowel disease (ulcerative colitis or Crohn disease) or any other gastrointestinal disorder causing chronic nausea, vomiting, or diarrhea (defined as greater than or equal to 2 CTCAE grade 2)
• Evidence of interstitial lung disease or active, non-infectious pneumonitis, or uncontrolled asthma Prior/Concomitant Therapy
• Prior STEAP1-targeted therapy
• Any anticancer therapy or immunotherapy within 4 weeks of start of first dose, not including LHRH/GnRH analogue (agonist/antagonist). Subjects on a stable bisphosphonate or denosumab regimen for greater or equal than 30 days prior to enrollment are eligible.
• Requirement for chronic systemic corticosteroid therapy (prednisone dose greater than 10 mg per day or equivalent) or any other immunosuppressive therapies (including anti TNF-alpha therapies) unless stopped (with adequate tapering) within 7 days prior to dosing 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.

Other Exclusions

• Male subjects with a female partner of childbearing potential who are unwilling to practice sexual abstinence (refrain from heterosexual intercourse) or use contraception during treatment and for an additional 6 months after the last dose of AMG 509. Refer to Section 12.5 for additional contraceptive information.
• Subject has known sensitivity to any components of AMG 509 to be administered during dosing.
• Subject likely to not be available to complete all protocol-required study visits or procedures, and/or to comply with all required study procedures (eg, Clinical Outcome Assessments) to the best of the subject and investigator's knowledge.
• History or evidence of any other clinically significant disorder, condition or disease (with the exception of those outlined above) that, in the opinion of the investigator or Amgen physician, if consulted, would pose a risk to subject safety or interfere with the study evaluation, procedures or completion.