Pevonedistat Alone and in Combination With Chemotherapy in Patients With Mesothelioma

Inclusion Criteria: Both cohorts: * Patients must have a histologically confirmed diagnosis of epithelioid, sarcomatoid, or mixed-type malignant pleural or peritoneal mesothelioma that is not amenable to surgery. * Patients must have measurable disease according to the modified RECIST criteria for pleural mesothelioma, or standard RECIST for peritoneal mesothelioma. Patients must have adequate tissue sample available for molecular profiling with MSK-IMPACT (archived tissue block or 15-20 unstained slides). Patients will sign a separate informed document (IRB #12-245) to allow this to be performed. * Patients must be at least 18 years of age. * Karnofsky performance status ≥ 70%. * Adequate renal function: serum creatinine ≤ 1.5 x ULN. * Clinical laboratory values within the following parameters (repeat if more than 7 days before the first dose): °Albumin \> 2.7 g/dL * Patients must have adequate hepatic function as defined by: * AST and ALT ≤ 2.5 x ULN * Total bilirubin ≤ upper limit of normal (ULN) except in patients with Gilbert's syndrome. Patients with Gilbert's syndrome may enroll if direct bilirubin ≤1.5 x ULN of the direct bilirubin. * Patients must have adequate bone marrow function as defined by: * Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L * Platelets ≥ 100 x 10\^9/L * Hemoglobin ≥ 9 g/dL. * Female patients who * Are postmenopausal for at least 1 year before the screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential: * Agree to practice 1 highly effective method and 1 additional effective (barrier) method of contraception, at the same time, from the time of signing the informed consent through 4 months after the last dose of study drug (female and male condoms should not be used together), or * Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.) * Male patients, even if surgically sterilized (i.e., status post vasectomy), who: * Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug (female and male condoms should not be used together), or * Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods for the female partner\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.) * Signed informed consent Cohort 1: * Patients must have received at least one and no more than four prior systemic therapy regimens. At least one of the regimens must have included pemetrexed and a platinum. * Patients must have MM that harbors an NF2 mutation believed to cause functional loss of the NF2 protein as determined by any CLIA lab certified NGS platform or NF2 loss must be documented by CLIA certified IHC. Cohort 2: * Patients must not have previously received treatment with chemotherapy for MM. * Patients must not have ≥ grade 2 peripheral neuropathy. * Patients must not have \> grade 2 hearing deficits. Exclusion Criteria: * Patients currently receiving radiation therapy, or who have received radiation within 2 weeks from the start of therapy. Patients who have had a major surgery or significant traumatic injury within 4 weeks of start of study drug, patients who have not recovered from the side effects of any major surgery (defined as requiring general anesthesia) or patients that may require major surgery during the course of the study. * Diagnosed or treated for another malignancy within 2 years before randomization or previously diagnosed with another malignancy and have any evidence of residual disease. Patients with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone resection. * Life-threatening illness unrelated to cancer. * Patients with uncontrolled coagulopathy or bleeding disorder. * Patients who have any severe and/or uncontrolled medical conditions or other conditions that could affect their participation in the study such as: * Known cardiopulmonary disease defined as: * Unstable angina * Congestive heart failure (New York Hear Association \[NYHA\] Class III or IV * Myocardial infarction (MI) within 6 months prior to first dose (patients who had ischemic heart disease such as ACS, MI and/or revascularization greater than 6 months before screening and who are without cardiac symptoms may enroll. * Cardiomyopathy * Clinically significant arrhythmia: * Polymorphic ventricular fibrillation or torsade de pointes. * Permanent atrial fibrillation \[a fib\], defined as continuous a fib ≥ 6 months. * Persistent a fib, defined as sustained a fib lasting \> 7 days and/or requiring cardioversion in the 4 weeks before screening * Grade 3 a fib defined as symptomatic and incompletely controlled medically, or controlled with device (e.g. pacemaker), or ablation * Patients with paroxysmal a fib or \< Gr 3 a fib for period of at least 6 months are permitted to enroll provided that their rate is controlled on a stable regimen. * Implantable cardioverter defibrillator * Moderate to severe aortic and/or mitral stenosis or other valvulopathy (ongoing) * Symptomatic pulmonary hypertension * Active infection requiring IV antibiotic, antiviral, or anti-fungal medications within 2 weeks of starting study drug. * Known history of HIV seropositivity * Known hepatitis B surface antigen seropositive or known or suspected active hepatitis C infection Note: Patients who have isolated positive hepatitis B core antibody (i.e., in the setting of negative hepatitis B surface antigen and negative hepatitis B surface antibody) must have an undetectable hepatitis B viral load. Patients who have positive hepatitis C antibody may be included if they have an undetectable hepatitis C viral load. * Known hepatic cirrhosis or severe pre-existing hepatic impairment * Uncontrolled high blood pressure (i.e., systolic blood pressure \> 180 mm Hg, diastolic blood pressure \> 95 mm Hg). * Prolonged rate corrected QT (QTc) interval ≥500 msec, calculated according to institutional guidelines. * Left ventricular ejection fraction (LVEF) \< 50% as assessed by echocardiogram or radionuclide angiography. * Known central nervous system (CNS) involvement. * Female patients who are both lactating and breastfeeding or have a positive serum pregnancy test during the screening period or a positive urine pregnancy test on Day 1 before first dose of study drug. * Female patients who intend to donate eggs (ova) during the course of this study or 4 months after receiving their last dose of study drug(s). * Male patients who intend to donate sperm during the course of this study or 4 months after receiving their last dose of study drug(s). * Patients with a currently active second malignancy requiring treatment. * Treatment with clinically significant metabolic enzyme inducers within 14 days before the first dose of the study drug. Clinically significant metabolic enzyme inducers are not permitted during this study.