Study of AMG 994 Monotherapy and AMG 994 and AMG 404 Combination Therapy in Participants With Advanced Solid Tumors

Inclusion Criteria: * Participant has provided informed consent/assent prior to initiation of any study specific activities/procedures. * Age ≥ 18 years at the time of signing informed consent. * Life expectancy of \> 3 months, in the opinion of the investigator. * Participant must have histologically or cytologically proven metastatic or locally advanced solid tumors of known MSLN expression who have relapsed after and/or are refractory to established and available therapies with known clinical benefit, for which: * No standard systemic therapy exists; or * Standard systemic therapy has failed or is not available. * Dose Expansion (Part 2): Participant must have one of the following malignancies: mesothelioma, pancreatic adenocarcinoma, MSLN positive NSCLC squamous cell carcinoma or adenocarcinoma, high grade serous ovarian carcinoma. * At least 1 measurable or evaluable lesion as defined by modified RECIST 1.1 guidelines. * Participants must be willing to undergo a biopsy prior to enrollment and during treatment with AMG 994. * Participants 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 central nervous system (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 non-serious CNS diseases that are asymptomatic and deemed irreversible (eg, peripheral neuropathy), 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 and has not had a seizure within 1 month prior to the screening visit. * Eastern Cooperative Oncology Group (ECOG) Performance Status of ≤ 2. * Hematologic function, as follows (transfusions or growth factor support must not be administered within 7 days prior to obtaining screening labs): * Absolute neutrophil count (ANC) ≥ 1.5 x 109/L * Platelet count ≥ 75 x 109/L * Hemoglobin ≥ 9 g/dL * Adequate renal laboratory assessments, as follows: • Estimated glomerular filtration rate based on Modification of Diet in Renal Disease (MDRD) calculation ≥ 45 mL/min/1.73 m2 * Hepatic function, as follows: * Total bilirubin (TBL) ≤ 1.5 x upper limit of normal (ULN) or ≤ 3 x ULN for participants with liver metastasis * Aspartate transaminase (AST) ≤ 3 x ULN or ≤ 5 x ULN for participants with liver metastasis * Alanine aminotransferase (ALT) ≤ 3 x ULN or ≤ 5 x ULN for participants with liver metastasis * Alkaline phosphatase ≤ 2.5 x ULN or ≤ 5 x ULN for participants with liver metastasis Exclusion Criteria: Disease Related * Primary brain tumor, untreated or symptomatic brain metastases and leptomeningeal disease. 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 ≥ 3 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. * Participants with NSCLC squamous cell carcinoma (Part 1), MSLN negative NSCLC squamous cell carcinoma (Part 2), or MSLN negative NSCLC adenocarcinoma (Part 2) once the participant has been screened for MSLN expression. * Participants with sarcomatoid mesothelioma and small cell lung cancer will be excluded from both the Dose Exploration (Part 1) and Dose Expansion (Part 2) parts of the study. * History of solid organ transplantation. * Major surgery within 28 days of study day 1. Prior/Concomitant Therapy * Anti-tumor therapy (radiotherapy, chemotherapy, antibody therapy, molecular targeted therapy, or investigational agent) within 21 days prior to study day 1. * Treatment with a checkpoint inhibitor within 9 weeks prior to study day 1. * 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 \> 10 mg prednisone daily or equivalent. Steroids with no minimal systemic effect (such as topical or inhalation) are permitted. 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). * Evidence of active or radiological sequelae of 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 results for human immunodeficiency virus (HIV). * Hepatitis B and C based on the following results: * 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. * Active infection requiring oral or intravenous therapy. * Active or history of any autoimmune disease or immunodeficiencies. Participants with diabetes Type 1, 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 \> class II), unstable angina, or cardiac arrhythmia requiring 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 noninvasive intervention AND there is agreement to allow by both the investigator and the Amgen Medical Monitor. * Any history of grade 3 or higher colitis, pneumonitis, or neurological toxicity OR * Unresolved toxicities from prior checkpoint inhibitor therapy, defined as not having resolved to CTCAE v5.0 grade 1. * Exception: - clinically stable hypothyroid status managed with hormone replacement therapy, is permitted Other Exclusions * Female participant is pregnant or breastfeeding or planning to become pregnant or breastfeed during treatment and for an additional 6 months after the last dose of AMG 994 and/or AMG 404. * Female participants of childbearing potential unwilling to use 1 highly effective method of contraception during treatment and for an additional 6 months after the last dose of AMG 994 and/or AMG 404. * Female participants of childbearing potential with a positive pregnancy test assessed at day 1 by a serum pregnancy test. * Male participants 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 8 months after the last dose of AMG 994 and/or AMG 404. * Male participants unwilling to abstain from donating sperm during treatment and for an additional 8 months after the last dose of AMG 994 and/or AMG 404. * Participant has known sensitivity to any of the products or components to be administered during dosing. * Participant likely to not be available to complete all protocol-required study visits or procedures, and/or to comply with all required study procedures to the best of the participant 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 participant safety or interfere with the study evaluation, procedures or completion.