Safety Study of Enoblituzumab (MGA271) in Combination With Pembrolizumab or MGA012 in Refractory Cancer

Inclusion Criteria: * To enroll on cohorts 1-4, participants must have a histologically-proven, previously treated, unresectable, locally advanced or metastatic mesothelioma, urothelial cancer, thyroid cancer, pancreatic cancer, ovarian cancer, colon cancer, prostate cancer, soft tissue sarcoma, triple negative breast cancer, renal clear cell cancer, melanoma, squamous cell cancer of the head and neck, or non-small cell lung cancer. * Participants on the melanoma cohort must have progressed on or after at least one anti-PD-L1 or anti- PD-1 containing therapy. * Participants on the SCCHN cohort must have progressed on or after platinum-based systemic therapy * Participants on the NSCLC cohort must have progressed on or after first line systemic therapy * Participants on the urothelial cancer cohort must have received at least one platinum-containing regimen and have progressed on or after an anti-PD-L1 or anti-PD-1 containing therapy * Measurable disease per RECIST 1.1 criteria * Easter Cooperative Oncology Group (ECOG) performance status 0 or 1 * Acceptable laboratory parameters and adequate organ reserve. Exclusion Criteria: * Patients with a history of symptomatic central nervous system metastases, unless treated and asymptomatic * Patients with history of autoimmune disease with certain exceptions such as vitiligo, resolved childhood atopic dermatitis, psoriasis not requiring systemic therapy within the past 2 years, patients with history of Grave's disease that are now euthyroid clinically and by lab testing * History of allogeneic bone marrow, stem cell, or solid organ transplant * Treatment with systemic cancer therapy or investigational therapy within 4 weeks of first study drug administration; radiation within 2 weeks; corticosteroids (greater than or equal to 10 mg prednisone or equivalent per day) or other immune suppressive drugs within 2 weeks of first study drug administration * Trauma or major surgery within 4 weeks of first study drug administration * History of clinically-significant cardiovascular disease; gastrointestinal perforation; gastrointestinal bleeding, acute pancreatitis or diverticulitis within 4 weeks of first study drug administration * Active viral, bacterial, or systemic fungal infection requiring parenteral treatment within 7 days of first study drug administration * Known history of hepatitis B or C infection or known positive test for hepatitis B surface antigen or core antigen, or hepatitis C polymerase chain reaction (PCR) * Known positive testing for human immunodeficiency virus or history of acquired immune deficiency syndrome * Known hypersensitivity to recombinant proteins, polysorbate 80, or any excipient contained in the drug or vehicle formulation for MGA271 or pembrolizumab.