Tivantinib in Treating Patients With Previously Treated Malignant Mesothelioma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed malignant pleural or peritoneal mesothelioma, epithelial, sarcomatoid, or mixed subtype; the patient's disease must be metastatic, recurrent, or unresectable * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam; pleural effusions and ascites are not considered measurable lesions * No more than two prior cytotoxic chemotherapy regimens; prior chemotherapy with pemetrexed is required; prior intrapleural cytotoxic agents (including bleomycin) are allowed, and are not counted as a cytotoxic chemotherapy; chemotherapy must have been completed at least 4 weeks prior; patients who have previously received radiation therapy are eligible provided that the only site of measurable disease is not located within the radiation therapy port; at least 4 weeks must have elapsed from completion of the radiation therapy and all signs of toxicity must have resolved * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Life expectancy of greater than 3 months * Hemoglobin \>= 9.0 g/dL * White blood cells (WBC) \>= 3,000/mcL * Absolute neutrophil count \>…