Alisertib and Pembrolizumab for the Treatment of Patients With Rb-deficient Head and Neck Squamous Cell Cancer

Inclusion Criteria - phase II only 1. Histologically or cytological confirmed diagnosis of Rb-deficient HNSCC for which no standard curative therapy is available. 2. Rb deficient HNSCC includes CLIA-certified testing confirming one of the following: A. HPV positive as determined by any one of the following: p16 immunohistochemistry (IHC), HPV RNA in situ hybridization (ISH), RNAscope (mRNA ISH), DNA ISH, DNA PCR, or qRT PCR. B. No Rb protein expression in the tumor as determined by IHC.41, 48 3. Progression on prior treatment with an anti-PD-1 antibody or an anti-PD-L1 antibody. A. Has received at least 2 doses of a PD-1/PD-L1 checkpoint blockade therapy. B. Clinical or radiographical progression has been documented within 12 weeks from the last dose of PD-1/PD-L1 checkpoint blockade therapy. Inclusion Criteria - phase I only 1\. Histologically or cytological confirmed diagnosis of an invasive solid tumor malignancy, for which no standard curative or life prolonging therapy is available. Inclusion Criteria - both phase I and phase II 1. Male or female patients ≥ 18 years of age. 2. ECOG performance status of ≤ 2 (see section 7.4). 3. Clinical laboratory values as specified below within 22 days before the first dose of study drug * Absolute neutrophil count (ANC) \> 1500/mm³ * Platelets \> 100,000/mm³ * Hgb \> 9 g/dL. Values must be obtained without need for myeloid growth factor or platelet transfusion support within 14 days, however, erythrocyte growth factor is allowed as per published ASCO guidelines. * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) * SGOT (AST) and SGPT (ALT)\< 2.5 x ULN. AST and/or ALT may be up to 5X ULN if with known liver mets or total 3 x ULN with direct bilirubin ≤ ULN in patients with well-documented Gilbert syndrome. * Adequate renal function as defined by calculated creatinine clearance ≥30 ml/min (Cockroft-Gault Formula, see Section 7.5). 4. Measurable disease according to RECIST version 1.1. 5. Voluntary written consent must be given before performance of any study related procedure not part of standard of care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care. 6. Patients must be able to either swallow alisertib enteric coated tablets, swallow alisertib oral solution formulation, or administer alisertib oral solution formulation via a feeding tube that terminates in the stomach. 7. Willing to provide blood and tissue for correlative research purposes. 8. 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 of contraception and 1 additional effective (barrier) method at the same time, from the time of signing the informed consent through 120 days after the last dose of study drug, OR * Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[eg, calendar, ovulation, symptothermal, postovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together.) 9. Male patients, even if surgically sterilized (i.e., status postvasectomy), who: * Agree to practice effective barrier contraception during the entire study treatment period and through 120 after the last dose of study drug, 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. Female and male condoms should not be used together.) Exclusion Criteria: 1. Radiation therapy to more than 25% of the bone marrow. Whole pelvic radiation is considered to be over 25%. 2. Prior allogeneic bone marrow or organ transplantation. 3. Known gastrointestinal (GI) disease or GI procedures that could interfere with the oral absorption or tolerance of alisertib. Examples include, but are not limited to partial gastrectomy, history of small intestine surgery, and celiac disease. 4. Inability to swallow (or use a feeding tube to administer) oral medication or inability or unwillingness to comply with the administration requirements related to alisertib. 5. Known history of uncontrolled sleep apnea syndrome and other conditions that could result in excessive daytime sleepiness, such as severe chronic obstructive pulmonary disease; requirement for supplemental oxygen. 6. Requirement for constant administration of proton pump inhibitor, H2 antagonist, or pancreatic enzymes throughout the study. The intermittent use of H2-antagonists and antacids (including carafate) is only allowed within these guidelines: 1. H2 antagonists until D-1 and after the dosing of alisertib is done 2. Antacid formulations until 2 hours before doing and after 2 hours following dosing. 3. PPI is allowed until D-5 of first alisertib dose. PPIs are prohibited throughout the study 7. Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure (see Section 7.3), uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any ECG abnormality at Screening has to be documented by the investigator as not medically relevant. 8. Female subject who is pregnant or breast-feeding. Confirmation that the subject is not pregnant must be established by a negative urine or serum β-human chorionic gonadotropin (β-hCG) pregnancy test result obtained during screening. Pregnancy testing is not required for post-menopausal or surgically sterilized women. 9. Female patient who intend to donate eggs (ova) during the course of this study or 120 days after receiving their last dose of study drug(s). 10. Male patients who intend to donate sperm during the course of this study or 120 days after receiving their last dose of study drug(s). 11. Other severe acute or chronic medical or psychiatric condition, including uncontrolled diabetes, malabsorption, resection of the pancreas or upper small bowel, requirement for pancreatic enzymes, any condition that would modify small bowel absorption of oral medications, or laboratory abnormality that may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for enrollment in this study. 12. Diagnosed or treated for another invasive malignancy within 2 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy. 13. Has received any anti-cancer treatment including investigational agents within 21 days prior to first dose of alisertib. 14. Patients who receive gamma knife radiosurgery for brain metastases or whole brain radiation are eligible if gamma knife radiosurgery was completed \> 2 weeks before treatment is started or whole brain radiation was performed \> 4 weeks before treatment is started, and are clinically stable (not requiring steroids or anti-epileptic drugs). 15. Known hypersensitivity to any of the excipients of alisertib enteric coated tablets or severe reaction to any human monoclonal antibody. 16. Patients with a prior history of clinically significant metabolic acidosis (exclusion only for patients receiving alisertib oral solution). 17. Major surgery within 28 days prior to first dose of alisertib or persisting side effects that have not improved to NCI-CTCAE grade 1 or better. 18. Patients who are on (or will require) prolonged systemic corticosteroid treatment during the study except for replacement dosing for adrenal insufficiency. 19. Concurrent severe and/or uncontrolled medical conditions that would, in the investigator's judgment, contraindicate patient participation in the clinical study or require concomitant anti-cancer drugs (e.g. active or uncontrolled severe infection, chronic active hepatitis, immuno-compromised, acute or chronic pancreatitis, uncontrolled high blood pressure, interstitial lung disease). 20. Patients with active, known, diagnosed or suspected autoimmune disease. Patients suffering from vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune thyroiditis only requiring thyroid hormone replacement therapy, or psoriasis not requiring systemic treatment can be enrolled. 21. Patients diagnosed with active interstitial lung disease (ILD)/pneumonitis or a history of ILD/pneumonitis or another condition requiring immunosuppressive doses of systemic medication such as systemic corticosteroids or absorbed topical corticosteroids (doses ≥ 10 mg/day prednisone or equivalent) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical corticosteroids, adrenal replacement doses, or \< 10 mg daily prednisone or equivalent are permitted. 22. Administration of any live vaccine within 30 days before first dose of study drug. 23. Uncontrolled infection with human immunodeficiency virus (HIV), hepatitis B virus or hepatitis C virus, except for: Patients with HIV who have controlled infection (undetectable viral load and CD4 count above 350 cells/mm3 either spontaneously or on a stable antiviral regimen) are permitted; Patients with hepatitis B (HepBsAg+) virus who have controlled infection (serum hepatitis B virus DNA PCR that is below the limit of detection AND receiving antiviral therapy for hepatitis B) are permitted; Patients who are hepatitis C virus antibody positive (HCV Ab +) who have controlled infection (undetectable HCV RNA by PCR either spontaneously or in response to a successful prior course of anti-HCV therapy) are permitted. 24. Participating in another therapeutic clinical trial. 25. Prior immune-related adverse events (irAE) as follows: A. Any life-threatening irAE will not be eligible. B. Any grade irAE of the following types will not be eligible: * i. Nervous system irAE * ii. Ocular irAE * iii. Cardiovascular irAE * iv. Severe Cutaneous Adverse Reactions (SCAR) * v. Hematological irAE C. Any grade endocrine irAE will be eligible if replacement therapy can compensate for the resulting deficit. D. Grade ≥ 2 irAE of the following will not be eligible: * i. Colitis * ii. Hepatitis * iii. Bullous Dermatoses * iv. Pneumonitis * v. Musculoskeletal * vi. Renal E. Grade ≥ 3 cutaneous irAE will not be eligible. F. All irAEs must have resolved to Grade ≤ 1 at least 14 days before the planned first dose.