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 p…