AMG 404 in Patients With Advanced Solid Tumors

Inclusion Criteria: * Subject has provided informed consent prior to initiation of any study specific activities/procedures. * Age greater than or equal to 18 years old at the time of signing informed consent. * Life expectancy of greater than 3 months, in the opinion of the investigator * Subject must have histologically or cytologically confirmed metastatic or locally advanced solid tumors not amenable to curative treatment with surgery or radiation. * Cohort 7: participant must have one of the following tumor types: melanoma, small cell lung cancer, NSCLC (PD-L1 positive), head and neck squamous cell cancer (PD-L1 positive), urothelial (PD-L1 positive), gastric or GEJ adenocarcinoma (PD-L1 positive), esophageal (squamous, PD-L1 positive), cervical (PD-L1 positive), hepatocellular carcinoma, merkel cell carcinoma, squamous cell carcinoma of the skin, renal cell carcinoma (clear cell) subtypes of sarcoma (undifferentiated pleiomorphic / malignant fibrous histiocytoma, poorly differentiated and/or dedifferentiated liposarcoma, alveolar soft tissue sarcoma, angiosarcoma), thymic carcinoma, nasopharyngeal carcinoma (EBV positive), mesothelioma * Cohort 8: participant must be MSI-H or MMR-deficient * Cohort 9: participant must have NSCLC, PD-L1 positive, TPS ≥ 50%; not have EGFR or ALK or ROS1 genomic tumor aberrations and may not have received prior systemic treatment for the advanced disease (prior neoadjuvant, adjuvant, or concurrent chemoradiation is allowed). * At least 1 measurable as defined by modified RECIST 1.1 which has not undergone biopsy within 3 months of the screening scan. This lesion cannot be biopsied at any time during the study. Note: if there is only one lesion available for biopsy and radiographic assessment, it may be permitted to be biopsied after discussion with sponsor. * Subjects with treated brain metastases are eligible provided they meet the following criteria: Definitive therapy was completed at least 2 weeks prior to enrollment. No evidence of radiographic CNS progression or CNS disease following definitive therapy and by the time of study screening. Patients manifesting progression in lesions previously treated with stereotactic radiosurgery may still be eligible if pseudoprogression can be demonstrated by appropriate means and after discussion with the medical monitor. * Any CNS disease is asymptomatic, any neurologic symptoms due to CNS disease have returned to baseline or are deemed irreversible, the patient is off steroids for at least 7 days (physiologic doses of steroids are permitted), and the patient is off or on stable doses of anti-epileptic drugs for malignant CNS disease. * Eastern Cooperative Oncology Group (ECOG) Performance Status of less than or equal to 2. * Hematologic function, as follows without growth factor support within 2 weeks prior to study day 1: Absolute neutrophil count (ANC) greater than or equal to 1.0 x 10E9/L; Platelet count greater than or equal to 75 x 10E9/L; Hemoglobin greater than or equal to 9 g/dL (90 g/L). * Adequate renal laboratory assessments, as follows: Estimated glomerular filtration rate based on MDRD (Modification of Diet in Renal Disease) calculation . 60 ml/min/1.73 m\^2 for Cohorts 1, 2, and 4 Estimated glomerular filtration rate based on MDRD (Modification of Diet in Renal Disease) calculation \>= 45 ml/min/1.73 m\^2 for Cohorts 3, 6, 7, 8 and 9. * Hepatic function, as follows: Total bilirubin less than or equal to 1.5 x ULN or less than or equal to 3 x ULN for subjects with liver metastasis; AST less than or equal to 3 x ULN or less than or equal to' 5 x ULN for subjects with liver metastasis; ALT less than or equal to 3 x ULN or less than or equal to 5 x ULN for subjects with liver metastasis; Alkaline phosphatase less than or equal to 2.5 x ULN or less than or equal to 5 x ULN for subjects with liver metastasis (Note: elevated alkaline phosphatase is acceptable if it is due to non-hepatic associated pathology \[eg, bone disease\]). * Subjects enrolled to Cohorts 7-9 must submit tumor tissue sample. Fresh tumor biopsies may be performed if subject has a readily accessible tumor lesion and who consent to the biopsies. If fresh biopsies cannot be obtained, archival tumor samples are acceptable. Prior to enrollment it is required to determine that there is enough tumor tissue available to be sent to the central laboratory: Cohorts 7 and 9: Archival tissue collected up to 12 months prior to screening date is permitted. Biopsies collected between 12-18 months prior to screening are allowed upon discussion with the medical monitor. Subjects with EBV associated nasopharyngeal carcinoma may submit biopsy with EBV test results from within 36 months prior to screening; Cohort 8: Archival tissue with MSI-high/dMMR test results collected up to 36 months prior to screening is permitted. Exclusion Criteria: * Disease Related. Primary brain tumor, untreated or symptomatic brain metastases and leptomeningeal disease (exception: benign asymptomatic tumors are permitted). * Other Medical Conditions. 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 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 cervical carcinoma in situ without evidence of disease. Adequately treated breast ductal carcinoma in situ without evidence of disease. Prostatic intraepithelial neoplasia without evidence of prostate cancer. Adequately treated urothelial papillary noninvasive carcinoma or carcinoma in situ. Other malignancies which do not require systemic therapy, may be considered upon discussion with the medical monitor. * History of solid organ transplantation. * Major surgery within 28 days of study day 1. * Prior/Concomitant Therapy: Prior treatment with anti-programmed death 1 (PD-1), anti-PD-L1, CTLA-4 or other checkpoint inhibitor drugs * Anti-tumor therapy (radiotherapy, chemotherapy, antibody therapy, molecular targeted therapy, or investigational agent) within 21 days prior to study day 1. Note: Palliative radiotherapy is permitted. * Live vaccine therapy within 4 weeks prior to study drug administration. * Current treatment or within 14 days of day 1 with immunosuppressive corticosteroid defined as greater than 10 mg prednisone daily or equivalent. Corticosteroids with no or minimal systemic effect (such as topical or inhalation) are permitted. Note: Corticosteroids \> 10 mg prednisone used for management of contrast allergy for study scans is allowed. * Prior/Concurrent Clinical Study Experience: Currently receiving treatment in another investigational device or drug study, or less than 21 days prior to study day 1 since ending treatment on another investigational device or drug study(ies). * Diagnostic Assessments: Evidence of interstitial lung disease or active, non-infectious pneumonitis. * History of any immune-related colitis. Infectious colitis is allowed if evidence of adequate treatment and clinical recovery exists and at least 3 months interval observed since diagnosis of colitis. * History of allergic reactions or acute hypersensitivity reaction to antibody therapies. * Positive/Non-negative test for Human Immunodeficiency Virus (HIV). * Has known active Hepatitis B (eg, hepatitis B antigen \[HBsAg\] reactive) or Hepatitis C (eg, HCV RNA \[qualitative\] is detected). * Subject currently has an active infection requiring systemic therapy. * Active or history of any autoimmune disease or immunodeficiencies. Subjects with Type I diabetes, vitiligo, psoriasis, hypo- or hyper- thyroid disease not requiring immunosuppressive treatment are permitted. * Myocardial infarction within 6 months of study day 1, symptomatic congestive heart failure (New York Heart Association greater than class II), unstable angina, or cardiac arrhythmia requiring antiarrhythmic medication. * Unresolved toxicities from prior anti-tumor therapy, defined as not having resolved to Common Terminology Criteria for Adverse Events (CTCAE) version 5.0 grade 1, or are stable and well controlled with minimal, local, or non-invasive intervention AND there is agreement to allow by both the investigator and the Amgen Medical Monitor. * Other Exclusions: Males and females of reproductive potential who are unwilling to practice highly effective methods of birth control while on study through 6 months (females) and 8 months (males) after receiving the last dose of AMG 404.