Following the dose-escalation phase of the study, additional patients (in order to reach a total of 13 patients with MPM and 18 patients with NSCLC treated at MTD/recommended dose for phase Ib trials) will be accrued to the expansion stage of this trial, to assess the preliminary anti-tumor activity of Tivantinib in combination with Carboplatin (AUC 5) and Pemetrexed (500 mg/mq) primarily.