Atezolizumab, Pemetrexed Disodium, Cisplatin, and Surgery With or Without Radiation Therapy in Treating Patients With Stage I-III Pleural Malignant Mesothelioma

Inclusion Criteria: * STEP 1: NEOADJUVANT * Patient must have stage I-III malignant pleural mesothelioma that is deemed resectable and must be planning to undergo pleurectomy decortication (P/D) or extrapleural pneumonectomy (EPP) * Patient must have epithelioid or biphasic histology (sarcomatoid histology is excluded); histologic diagnosis and typing of mesothelioma requires at least a core needle biopsy or surgical biopsy of the pleura via thoracoscopy and small thoracotomy; cytology only will not be regarded as sufficient for the diagnosis * Patient must have computed tomography (CT) chest/abdomen/pelvis with contrast or fludeoxyglucose F-18 (FDG)-positron emission tomography (PET)/CT scan performed within 28 days prior to step 1 registration * Patients must have non-measurable or measurable disease documented by CT or magnetic resonance imaging (MRI); the CT from a combined PET/CT may be used to document only non-measurable disease unless it is of diagnostic quality; measurable disease must be assessed within 28 days prior to step 1 registration; non-measurable disease must be assessed within 42 days prior to step 1 registration; all disease must be assessed and documented on the RECIST 1.1 and modified RECIST baseline tumor assessment form * Patient must have undergone extended surgical staging including mediastinoscopy or endobronchial ultrasound; at minimum, samples must be obtained from the mediastinal stations 4R, 7 (subcarinal), and 4L; this surgical staging must b…