Testing the Addition of Targeted Radiation Therapy to Surgery and the Usual Chemotherapy Treatment (Pemetrexed and Cisplatin [or Carboplatin]) for Stage I-IIIA Malignant Pleural Mesothelioma

Inclusion Criteria: PRIOR TO STEP 1 REGISTRATION - ALL PATIENTS * Pathologically (histologically or cytologically) confirmed diagnosis of epithelioid or biphasic malignant pleural mesothelioma (MPM) * Imaging proof of clinical stage (American Joint Committee on Cancer \[AJCC\] 8th edition) I-IIIA MPM by PET/CT; * Diagnostic volumetric CT scan of the chest is preferred; however, the CT portion of the PET/CT may be used if CT imaging is of diagnostic quality * MPM is amenable to resection by P/D as determined by a thoracic surgeon * History/physical examination within 42 days prior to Step 1 Registration * Eastern Cooperative Oncology Group (ECOG) Performance Status 0-1 within 42 days prior to Step 1 Registration * Required Initial Laboratory Values prior to study entry (must be at least 14 days after last infusion of pre-study entry neoadjuvant therapy, if given): * Absolute neutrophil count ≥1500 cells/mm3; * Platelets ≥100,000 cells/mm3; * Hemoglobin ≥ 8.0 g/dL; * Serum total bilirubin ≤ 1.5 X ULN (upper limit of normal); * Aspartate transferase (AST) (serum glutamic-oxaloacetic transaminase (SGOT)) and alanine transaminase (ALT) (serum glutamic-oxaloacetic transaminase (SGPT)) ≤ 3.0 X ULN; * Creatinine clearance ≥45 mL/min by the Cockcroft-Gault (C-G) equation * Negative serum pregnancy test within 14 days of Step 1 Registration for women of childbearing potential * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. Note: HIV testing is not required for eligibility for this protocol. * The patient or a legally authorized representative must provide study-specific informed consent prior to study entry PRIOR TO STEP 1 REGISRATION - PATIENTS WHO RECEIVED SYSTEMIC THERAPY BEFORE STUDY ENTRY * The following systemic therapy and immunotherapy combinations are permissible: 1) cisplatin/carboplatin + pemetrexed; 2) cisplatin/carboplatin + pemetrexed + anti-PD-1/L1 agents; and 3) ipilimumab/nivolumab. * Patients must have received at least 2 cycles of neoadjuvant systemic therapy PRIOR TO STEP 2 RANDOMIZATION - ALL PATIENTS * No evidence of progression as defined by PET/CT within 30 days prior to Step 2 randomization. * Patients must have received at least 2 cycles of systemic therapy and undergone a pleurectomy/decortication with the goal of macroscopic complete resection; * ECOG Performance Status 0-1 within 30 days prior to Step 2 Randomization * History/physical examination within 30 days prior to Step 2 Randomization Exclusion Criteria: PRIOR TO STEP 1 REGISTRATION - ALL PATIENTS * Pregnancy or women who are breastfeeding and unwilling to discontinue. * Participants of childbearing potential (participants who may become pregnant or who may impregnate a partner) unwilling to use highly effective contraceptives during and for six months after end of treatment because the treatment in this study may be significantly teratogenic. * Diagnosis of sarcomatoid mesothelioma * Severe, active co-morbidity defined as follows: * New York Heart Association (NYHA) class III or IV heart failure * Chronic obstructive pulmonary disease (COPD) requiring chronic oral steroid therapy of \> 10 mg prednisone daily or equivalent at the time of registration. Inhaled corticosteroids are allowed; * Unstable angina requiring hospitalization and/or transmural myocardial infarction within the last 3 months; * Interstitial lung disease; * Hemodialysis or peritoneal dialysis; * Concurrent active malignancy (with the exception of current or prior non-melanomatous skin cancer or low-grade malignancies followed observantly for which treatment has not or does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen) * If evidence of disease \< 3 years, institution must consult with the principal investigator, Andreas Rimner, Doctor of Medicine (MD) * Hepatic impairment defined by ChildPugh class (ChildPugh class B \& C); * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy within 30 days prior to registration, if indicated. Note: HBV viral testing is not required for eligibility for this protocol * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load within 30 days prior to registration * • Active lung infection requiring IV antibiotics * Patients on immunosuppressive therapy, for example history of organ or bone marrow transplant or other hematologic disorders that are expected to compromise life expectancy or tolerance of treatment; * Prior nephrectomy on the contralateral side of MPM * Ipsilateral thoracic electronic implant, e.g. pacemaker, defibrillator, unless switched to the contralateral side prior to initiation of radiation therapy (RT) * Prior thoracic radiation therapy (patients with prior thoracic RT cannot be planned to 50-60 Gy without exceeding normal tissue constraints) * Use of bevacizumab or other antiangiogenic therapy to treat current mesothelioma (due to potential for increased complications from local therapy). * For patients who received neoadjuvant systemic therapy prior to study entry, surgery planned to occur greater than 8 weeks following neoadjuvant systemic therapy PRIOR TO STEP 2 RANDOMIZATION - ALL PATIENTS * Supplemental oxygen use * Third space fluid that cannot be controlled by drainage or insufficient lung expansion after P/D (this prevents targeting the pleura without exceeding normal tissue constraints) * Prior intrapleural therapy (i.e. intrapleural chemotherapy, photodynamic therapy); pleurodesis is permitted * Bulky residual disease in the major fissure preventing pleural IMRT * Patients who have undergone extrapleural pneumonectomy * Patients with active infection that requires systemic I.V. antibiotics, antiviral, or antifungal treatments