Pleurectomy/Decortication (Neo) Adjuvant Chemotherapy and Intensity Modulated Radiation Therapy to the Pleura in Patients With Locally Advanced Malignant Pleural Mesothelioma

Inclusion Criteria: * Provide written informed consent to participate on the study * Patients must have a pathologically confirmed diagnosis either at MSKCC or at the participating site of stage I-III malignant pleural mesothelioma * Epithelioid or biphasic histology subtype (Note: patients with biphasic histology can have \< 10% sarcomatoid) * No evidence of metastatic disease. * Patient age ≥ 18 years but ≤ 80 years at the time of consent. * Karnofsky performance status ≥ 80% * Pulmonary Function Tests: 1. For all patients: DLCO \> 40% predicted (corrected for Hgb) 2. For patients enrolled post-P/D, only: FEV1 \>/= 35% (corrected for Hgb) (Note: patients enrolled prior to P/D will have PFTs repeated pre-IMRT. If this criteria is not met, they will be removed from study) * In cases of concern about decreased renal function and potential high radiation dose to the kidneys, an optional nuclear medicine kidney function scan may be performed prior to radiation therapy to determine the functional contribution of each kidney. * Patient enrolled prior to chemotherapy must have adequate organ function as indicated by the following laboratory values: 1. Absolute neutrophil count ≥1.5 K/mcL 2. Platelets ≥100 K/mcL 3. Serum total bilirubin ≤ 1.5 X ULN 4. AST (SGOT) or ALT (SGPT) ≤ 3.0 X ULN Note: patients enrolled after chemotherapy do not have to meet the above criteria Exclusion Criteria: * \> 10% Sarcomatoid or desmoplastic histology * Continuous oxygen use * Prior nephrectomy on the contralateral side of MPM * Prior intrapleural therapy (except pleurodesis) or intrapleural therapy at the time of P/D (i.e.: intrapleural chemotherapy, photodynamic therapy, intrapleural betadine) * Prior thoracic radiation therapy preventing hemithoracic pleural IMRT * Bulky disease in the fissure preventing lung-sparing pleural IMRT * Patients undergoing extrapleural pneumonectomy * Patients with an active infection that require systemic antibiotics, antiviral, or antifungal treatments * Patients with a concurrent active malignancy (except squamous or basal cell carcinoma of the skin) * Patients with serious unstable medical illness * Presence of third space fluid that cannot be controlled by drainage * For patients who develop or have baseline clinically significant pleural effusions before or during initiation of pemetrexed therapy; consideration should be given to drain the effusion prior to chemotherapy administration * No acute congestive heart failure * Pregnant or lactating women * Men or women not using effective contraception Reproductive risks Patients should not become pregnant or father a baby while on this study because the drugs in this study can affect an unborn baby. Women should not breast-feed a baby while on this study. Women of childbearing age will be counseled to use birth control while on this study.