3. MPM tumor sample for determination of ASS1 status. ASS1-deficiency is not required for study entry at study start, but tumor sample for ASS1 status is required. This study will employ an adaptive biomarker-driven design with an interim analysis to be conducted at the end of the phase 2 portion. The interim analysis will evaluate the treatment effect of ADI PEG 20 in combination with pemetrexed and cisplatin on overall survival (OS) in the overall population (biphasic and sarcomatoid histology patients) and pre-defined subpopulation of biomarker-positive patients (ASS1-deficient subpopulation). Thus ASS1 deficiency may be required for the phase 3 portion of the study, pending the interim analysis. ASS1-deficiency, demonstrated on tissue specimen (cytospin samples are not acceptable), will be defined in the laboratory manual. If archived tissue is not sufficient or not available, then tissue must be obtained by biopsy.