Pembrolizumab in Treating Patients With Malignant Mesothelioma

Inclusion Criteria: * Histologically or cytologically confirmed pleural or peritoneal malignant mesothelioma, epithelial, sarcomatoid, or biphasic subtypes * Disease progression on or after pemetrexed and cis- or carboplatin * ONLY FOR PART B - PD-L1 selection should a PD-L1 expression threshold have been defined in Part A and potentially additional mesothelioma trial data; there will be no PD-L1/biomarker selection for Part A * No more than 2 prior lines of cytotoxic therapy, which should have included pemetrexed and a platinum * Enrollment of treatment naïve patients who refuse standard chemotherapy or are intolerant may be permissible if reviewed and deemed clinically appropriate by the principal investigator (PI) * Be willing and able to provide written informed consent for the trial * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 for peritoneal mesothelioma, and modified RECIST for pleural mesothelioma * Have provided tissue from an archival tissue sample or newly obtained core or excisional biopsy of a tumor lesion; while 20 unstained slides or a tumor block are preferred, at least 14 unstained slides are requested for analysis; PI approval for a lower number of slides is acceptable * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL * Serum creatinine =\< 1.5 X upper limit …