MLN9708 and Vorinostat in Patients With Advanced p53 Mutant Malignancies

Inclusion Criteria: 1. Male or female patients 18 years or older. 2. Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care. 3. 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 2 effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug, AND • Must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, OR • Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception.) 4. Male patients, even if surgically sterilized (ie, status post-vasectomy), must agree to one of the following: • Agree to practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug, OR • Must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, OR • Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence (eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception.) 5. Patients must have a diagnosis with solid tumors and lymphomas, either refractory to standard therapy or for which no effective standard therapy that conveys clinical benefit. 6. Patients must have a p53 mutation which is defined as cytoplasmic positivity by immunohistochemistry and/or next gene mutation sequencing. 7. Eastern Cooperative Oncology Group (ECOG) performance status and/or other performance status 0, 1, or 2. 8. Patients must meet the following clinical laboratory criteria:Absolute neutrophil count (ANC) \>/= 1,000/mm\^3 and platelet count \>/= 75,000/mm\^3. Platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment.Total bilirubin \</= 1.5 x the upper limit of the normal range (ULN).Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \</= 3 x ULN.Calculated creatinine clearance \>/= 30 mL/min. 9. Patients may receive local palliative radiation therapy immediately before or during the treatment if the radiation therapy is not delivered to the sole target lesions. 10. Measurable or evaluable disease will be included as assessed by RECIST 1.1. Exclusion Criteria: 1. Female patients who are lactating or have a positive blood pregnancy test during the screening period. 2. Failure to have fully recovered (ie, \</= Grade 1 toxicity) from the reversible effects of prior chemotherapy. 3. Major surgery within 14 days before first dose of study drug.. 4. Radiotherapy within 14 days before first dose of study drug. If the involved field is small, 7 days will be considered a sufficient interval between treatment and study initiation. 5. Active uncontrolled central nervous system involvement. 6. Infection requiring systemic antibiotic therapy or other serious infection within 14 days before first dose of study drug. 7. Evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, uncontrolled cardiac arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial infarction within the past 6 months. 8. Systemic treatment, within 14 days before the first dose of MLN9708, with strong inhibitors of CYP1A2 (fluvoxamine, enoxacin, ciprofloxacin), strong inhibitors of CYP3A (clarithromycin, telithromycin, itraconazole, voriconazole, ketoconazole, nefazodone, posaconazole) or strong CYP3A inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or use of Ginkgo biloba or St. John's wort. 9. Ongoing or active systemic infection, active hepatitis B or C virus infection, or known human immunodeficiency virus (HIV) positive. 10. Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol. 11. Known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent. 12. Known GI disease or GI procedure that could interfere with the oral absorption or tolerance of MLN9708 including difficulty swallowing. 13. Diagnosed or treated for another malignancy within 2 years before first dose of study drug. 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 complete resection. 14. Patient has \>/= Grade 2 peripheral neuropathy 15. Participation in other clinical trials, including those with other investigational agents not included in this trial, within 21days of the start of this trial and throughout the duration of this trial.