QUILT-3.090: NANT Squamous Cell Carcinoma (SCC) Vaccine: Subjects With SCC Who Have Progressed

Inclusion Criteria: 1. Age ≥ 18 years. 2. Able to understand and provide a signed informed consent that fulfills the relevant IRB or Independent Ethics Committee (IEC) guidelines. 3. Histologically-confirmed HNSCC or squamous NSCLC with progression on or after platinum-based chemotherapy and anti-PD-1/PD-L1 therapy. 4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2. 5. Have at least 1 measurable lesion of ≥ 1.0 cm. 6. Must have a recent formalin-fixed, paraffin-embedded (FFPE) tumor biopsy specimen following the conclusion of the most recent anticancer treatment. If an historic specimen is not available, the subject must be willing to undergo a biopsy during the screening period, if considered safe by the Investigator. If safety concerns preclude collection of a biopsy during the screening period, a tumor biopsy specimen collected prior to the conclusion of the most recent anticancer treatment may be used. 7. Must be willing to provide blood samples prior to the start of treatment on this study. 8. Must be willing to provide a tumor biopsy specimen 8 weeks after the start of treatment, if considered safe by the Investigator. 9. Ability to attend required study visits and return for adequate follow-up, as required by this protocol. 10. Agreement to practice effective contraception for female subjects of child-bearing potential and non-sterile males. Female subjects of child-bearing potential must agree to use effective contraception for up to 1 year after completion of therapy, and non-sterile male subjects must agree to use a condom for up to 4 months after treatment. Effective contraception includes surgical sterilization (eg, vasectomy, tubal ligation), two forms of barrier methods (eg, condom, diaphragm) used with spermicide, intrauterine devices (IUDs), and abstinence. Exclusion Criteria: 1. Serious uncontrolled concomitant disease that would contraindicate the use of the investigational drug used in this study or that would put the subject at high risk for treatment-related complications. 2. Systemic autoimmune disease (eg, lupus erythematosus, rheumatoid arthritis, Addison's disease, or autoimmune disease associated with lymphoma). 3. History of organ transplant requiring immunosuppression. 4. History of or active inflammatory bowel disease (eg, Crohn's disease, ulcerative colitis). 5. Inadequate organ function, evidenced by the following laboratory results: 1. Absolute neutrophil count \< 1,000 cells//mm\^3. 2. Uncorrectable grade 3 anemia (hemoglobin \< 8 g/dL). 3. Platelet count \< 75,000 cells/mm\^3. 4. Total bilirubin greater than the upper limit of normal (ULN; unless the subject has documented Gilbert's syndrome). 5. Aspartate aminotransferase (AST \[SGOT\]) or alanine aminotransferase (ALT \[SGPT\]) \> 2.5 × ULN (\> 5 × ULN in subjects with liver metastases). 6. Alkaline phosphatase levels \> 2.5 × ULN (\> 5 × ULN in subjects with liver metastases, or \>10 × ULN in subjects with bone metastases). 7. Serum creatinine \> 2.0 mg/dL or 177 μmol/L. 8. Serum anion gap \> 16 mEq/L or arterial blood with pH \< 7.3. 6. Uncontrolled hypertension (systolic \> 160 mm Hg and/or diastolic \> 110 mm Hg) or clinically significant (ie, active) cardiovascular disease, cerebrovascular accident/stroke, or myocardial infarction within 6 months prior to first study medication; unstable angina; congestive heart failure of New York Heart Association grade 2 or higher; or serious cardiac arrhythmia requiring medication. Subjects with uncontrolled hypertension should be medically managed on a stable regimen to control hypertension prior to study entry. 7. Serious myocardial dysfunction defined by ECHO as absolute left ventricular ejection fraction (LVEF) 10% below the institution's lower limit of predicted normal. 8. Dyspnea at rest due to complications of advanced malignancy or other disease requiring continuous oxygen therapy. 9. Positive results of screening test for human immunodeficiency virus (HIV). 10. Current chronic daily treatment (continuous for \> 3 months) with systemic corticosteroids (dose equivalent to or greater than 10 mg/day methylprednisolone), excluding inhaled steroids. Short-term steroid use to prevent IV contrast allergic reaction or anaphylaxis in subjects who have known contrast allergies is allowed. 11. Known hypersensitivity to any component of the study medication(s). 12. Subjects taking any medication(s) (herbal or prescribed) known to have an adverse drug reaction with any of the study medications. 13. Concurrent or prior use of a strong cytochrome P450 (CYP)3A4 inhibitor (including ketoconazole, itraconazole, posaconazole, clarithromycin, indinavir, nefazodone, nelfinavir, ritonavir, saquinavir, telithromycin, voriconazole, and grapefruit products) or strong CYP3A4 inducers (including phenytoin, carbamazepine, rifampin, rifabutin, rifapentin, phenobarbital, and St John's Wort) within 14 days before study day 1. 14. Concurrent or prior use of a strong CYP2C8 inhibitor (gemfibrozil) or moderate CYP2C8 inducer (rifampin) within 14 days before study day 1. 15. Participation in an investigational drug study or history of receiving any investigational treatment within 30 days prior to screening for this study, except for testosterone-lowering therapy in men with prostate cancer. 16. Assessed by the Investigator to be unable or unwilling to comply with the requirements of the protocol. 17. Concurrent participation in any interventional clinical trial. 18. Pregnant and nursing women.