AMG 102, Pemetrexed Disodium, and Cisplatin in Treating Patients With Malignant Pleural Mesothelioma

Inclusion Criteria: * Histologically and cytologically confirmed malignant mesothelioma of the pleura * All subtypes allowed * Disease not amenable to curative surgery * Measurable disease * Patients with disease not measurable by standard RECIST criteria (i.e., pleural rinds/thickening only) allowed * Pleural effusions or positive bone scans are not considered measurable * No prior radiotherapy to the target lesion or measurable lesion unless the site has subsequent evidence of progression * Patients who have undergone pleurodesis allowed * Post-pleurodesis CT scan required * No known or suspected brain metastases * ECOG performance status 0-1 * ANC ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Total bilirubin ≤ 1.5 times upper limit of normal (ULN) * Alkaline phosphatase ≤ 1.5 times ULN * ALT and AST ≤ 1.5 times ULN * Albumin ≥ 2.5 g/dL * Creatinine clearance ≥ 45 mL/min OR serum creatinine ≤ 1.5 times ULN * Able to take folic acid and vitamin B12 * Not pregnant or nursing * Negative pregnancy test * Fertile patients must agree to use effective contraception * No active infection or serious concomitant systemic disorder in compatible with the study * No thrombosis or vascular ischemic events within the last 12 months, including any of the following: * Deep venous thrombosis * Pulmonary embolism * Transient ischemic attack * Cerebral infarction * Myocardial infarction * No peripheral edema ≥ grade 3 * No serious or non-healing wounds * No second primary malignancy except in situ carcinoma of the cervix or breast, other in situ malignancies, adequately treated basal cell carcinoma of the skin, or other malignancy within the past 3 years with no evidence of recurrence * No concurrent antiretroviral therapy for HIV-positive patients * At least 4 weeks since prior radiotherapy * More than 30 days since major surgery procedures or \> 14 days since any minor surgical procedure and recovered * Central venous catheter placement, fine-needle aspiration, thoracentesis, or paracentesis are not considered major or minor surgical procedures * No prior systemic chemotherapy for mesothelioma * No prior intracavity cytotoxic drugs or immunomodulators (unless for the purpose of pleurodesis) * No prior anti-HGF monoclonal antibody AMG 102, other c-MET, or HGF inhibitors * No prior or concurrent anticoagulation therapy within the past 7 days * Low-dose Coumadin-type anticoagulants or low-molecular weight heparin for prophylaxis against central venous catheter thrombosis allowed * No investigational agents within the past 4 weeks