A Study of AMG 757 in Participants With Neuroendocrine Prostate Cancer

Inclusion Criteria (Part 1: Dose Exploration and Part 2: Dose Expansion): * Participant has provided informed consent prior to initiation of any study specific activities/procedures. * Men aged ≥ 18 years at time of signing the informed consent. * Metastatic de novo or treatment-emergent neuroendocrine prostate cancer (NEPC) defined by histology, immunohistochemistry, or genomic analyses of baseline tumor tissue (by local assessment) or circulating tumor DNA (ctDNA) (by local assessment) as per protocol * At least 1 line of prior systemic treatment per protocol. * Participants with treatment-emergent NEPC or de novo NEPC with histologic evidence of prostate cancer with neuroendocrine differentiation without a history of bilateral orchiectomy are required to remain on luteinizing hormone-releasing hormone (LHRH) analogue therapy during the course of protocol therapy * Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 per Prostate Cancer Working Group 3 (PCWG3) modifications * Eastern Cooperative Oncology Group (ECOG) Performance Status of ≤ 2 * Participants with treated brain metastases are eligible provided they meet defined criteria * Adequate organ function as defined in protocol Exclusion Criteria (Part 1: Dose Exploration and Part 2: Dose Expansion): * History of other malignancy within the past 2 years, with exceptions: * Malignancy treated with curative intent and with no known active disease present for ≥ 2 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 non-muscle invasive urothelial carcinoma * History or presence of hematological malignancies unless curatively treated with no evidence of disease ≥ 2 years * Untreated or symptomatic brain metastases and leptomeningeal disease * Anti-tumor therapy within 28 days of study day 1; concurrent use of hormone deprivation therapy for hormone refractory prostate cancer is permitted; participants on a stable bisphosphonate or denosumab prior to study day 1 are eligible Exceptions: * Participants who received conventional chemotherapy are eligible if at least 14 days have elapsed and if all treatment-related toxicities have resolved to Grade ≤ 1 * Prior palliative radiotherapy must have been completed at least 7 days before the first dose of tarlatamab * Participants who received androgen signaling inhibitor are eligible if at least 14 days have elapsed and if all treatment-related toxicity has been resolved to Grade ≤ 1 * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior study day 1 * Active autoimmune disease requiring systemic treatment within the past 2 years * Known positive test for human immunodeficiency virus (HIV) or hepatitis * Unresolved toxicities from prior anti-tumor therapy, defined as not having resolved to Common Terminology Criteria for Adverse Events (CTCAE) version 4.0 grade 0 or 1 (with the exception of alopecia or toxicities that are stable and well-controlled) * History of hypophysitis or pituitary dysfunction * Has evidence of interstitial lung disease or active, non-infectious pneumonitis. * Participants on prior delta-like ligand 3 (DLL3)-targeted therapy may be eligible if discussed with Amgen Medical Monitor prior to enrollment * Evidence of severe acute respiratory syndrome coronavirus 2 (SARS-COV2) infection unless agreed upon with Medical Monitor and with no acute symptoms of coronavirus disease 2019 (COVID19) disease within 14 days prior to first dose of investigational product (counted from day of positive test for asymptomatic participants).