Trial of a Personalized and Adaptive Neoantigen Dose-Adjusted Vaccine Concurrently With Pembrolizumab

Inclusion Criteria for Vaccine Generation: 1. Subject must sign an institutional review board (IRB) approved informed consent to undergo tissue procurement and HIPAA authorization for release of personal health information. 2. Subject must have a previously treated, histologically confirmed squamous non-small cell lung cancer and head and neck squamous cell carcinoma where cure is either not possible or curative modality therapy is declined by the subject. 3. Subject has adequate archival tumor tissue for sequencing for vaccine generation. 4. Subject has Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 1. 5. Subject has adequate bone marrow function as demonstrated by: * Absolute neutrophil count (ANC) ≥1.5 x 10\^9/L * Absolute lymphocyte count (ALC) ≥1.0 x 10\^9/L * Hemoglobin \>8 g/dL (use of transfusion to reach this threshold prior to study initiation is acceptable) * Platelet count ≥100 x 10\^9/L 6. Subject has radiographically measurable according to RECIST 1.1 and iRECIST. 7. Subjects must per RECIST 1.1 have stable disease, mixed response, oligoprogressive state (defined as disease progression at a limited number of anatomic sites, with continued response or stable disease at other sites of disease) or non-threatening progression (progression that fits a clinical pattern where the treating physician believes that PD-1 therapy post-progression is appropriate (e.g. multiple sub-centimeter nodules that do not compromise the bronchus)) on a PD-1, PDL-1 or PD-1/L containing regimen. 8. Subject must meet the following criteria: For squamous non-small cell lung cancer (NSCLC): * Tumor expressing PD-L1 (Tumor Proportion Score/TPS ≥1%) as determined by an FDA-approved test, with no EGFR or ALK genomic tumor aberrations * Subjects with EGFR or ALK genomic tumor aberrations should have disease progression on FDA-approved therapy for these aberrations. Squamous cell carcinoma of head and neck (SCCHN): * As 1st line treatment for tumors expressing PD-L1 \[Combined Positive Score (CPS) ≥1\] as determined by an FDA-approved test * As non-1st line treatment for recurrent or metastatic HNSCC with disease progression on or after platinum containing chemotherapy 9. Age ≥18 years. 10. Female subject of childbearing potential must agree to use adequate contraception during the study. Adequate contraception is defined by the concomitant use of at least 2 effective methods of contraception from the time of informed consent until 90 days after pembrolizumab or PANDA-VAC discontinuation, whichever is longer. The two contraception methods can be comprised of two barrier methods, or a barrier method plus a hormonal method or an intrauterine device that meets \<1% failure rate for protection from pregnancy in the product label. Females of non-childbearing potential are those who are postmenopausal greater than 1 year or who have had a bilateral tubal ligation or hysterectomy or bilateral oophorectomy. Female subjects must refrain from egg cell donation while on pembrolizumab or PANDA-VAC and for at least 90 days after the last dose of investigational product, based on whichever product was last given. 11. Male subjects with female partners must have had a prior vasectomy or agree to use an adequate method of contraception (i.e., double barrier method: condom plus spermicidal agent) starting with the first dose of pembrolizumab through 90 days after the last dose of pembrolizumab or PANDA-VAC, whichever is longer. Male subjects should agree to refrain from sperm donation while taking pembrolizumab and/or PANDA-VAC and for at least 90 days after the last dose of pembrolizumab or PANDA-VAC, whichever is longer. Should a female partner of a male subject become pregnant or suspect she is pregnant while participating in the study, he should inform his treating physician and the female partner should call her physician immediately. 12. Subject is willing and able to comply with the protocol including undergoing treatment and scheduled visits and examinations. 13. Subject is willing to consent to study-required blood draws and consent for the use of any residual material from biopsy or prior resections for vaccine generation and correlative studies. 14. Subject is willing to consent to a mandatory biopsy that is required for adapted vaccine generation and correlative studies if the subject has partial response, stable disease, mixed response, or oligoprogressive state following the full series of five priming and two booster vaccinations. 15. Subject must have recovered from all reversible acute toxic effects of the previous cancer treatment regimen (other than alopecia) to Grade ≤ 1 or baseline. Exclusion Criteria for Vaccine Generation: 1. Subject is currently participating in or has participated in a study of an investigational agent within 4 weeks of study pembrolizumab treatment initiation. 2. Subject has active infection requiring systemic therapy. 3. Subject is pregnant or breastfeeding (Note: breast milk cannot be stored for future use while the mother is being treated on the study). 4. Subject has a known additional malignancy that is active and/or progressive requiring treatment; exceptions include basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer for which the subject has been disease-free for at least five years. 5. Subject has active central nervous system (CNS) metastases. Treated metastases without evidence of progression will be allowed. Asymptomatic, subcentimeter metastases not requiring treatment will be allowed. Any leptomeningeal disease will be excluded. 6. Subject is currently using systemic corticosteroids at doses ≥10mg prednisone daily or its equivalent, or other immunosuppressive medications including, but not limited to methotrexate, azathioprine, calcineurin inhibitor, and TNF-α blockers. 7. Subject has known human immunodeficiency virus (HIV), hepatitis C virus (HCV) or evidence of active hepatitis B virus (HBV). 8. Subject has a history of primary immunodeficiency. 9. Subject has a history of organ transplant, bone marrow transplant or hematopoietic stem cell transplantation. 10. Subject has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. 11. Subject has received a live attenuated vaccines within 30 days of on study pembrolizumab dosing. Inactivated vaccines, such as the injectable influenza vaccine, are permitted. 12. Subject has any condition that, in the opinion of the investigator, would interfere with evaluation of study treatment or interpretation of subject safety or study results. 13. Subject is not a good candidate for treatment with pembrolizumab and PANDA-VAC per investigator's discretion. Eligibility Criteria for Vaccination: 1. Subject must sign written informed consent to enroll in the PANDA-VAC therapy trial. 2. Subject must have completed at least two cycles of standard of care therapy with pembrolizumab. 3. Subject has Eastern Cooperative Oncology Group (ECOG) performance status of ≤2. 4. Subject has radiographically measurable disease according to RECIST 1.1 and iRECIST. 5. Subjects must per RECIST 1.1 have stable disease, mixed response, oligoprogressive state (defined as disease progression at a limited number of anatomic sites, with continued response or stable disease at other sites of disease) or progressive disease. 6. Subject has adequate bone marrow function as demonstrated by: * Absolute neutrophil count (ANC) ≥1.5 x 10\^9/L * Absolute lymphocyte count (ALC) ≥0.5 x 10\^9/L * Hemoglobin \>8 g/dL (use of transfusion to reach this threshold prior to study initiation is acceptable) * Platelet count ≥50 x 10\^9/L 7. Subject has adequate hepatic and renal function as demonstrated by: * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x upper limit of normal (ULN) (unless liver metastases are present, in which case they must be ≤ 5 x ULN); * Total serum bilirubin ≤1.5 mg/dL (subjects with Gilbert's syndrome may be enrolled despite a total bilirubin level \>1.5 mg/dL if their conjugated bilirubin is \<1.5 × ULN)); * Creatinine clearance (CrCl) \>40mL/min as measured according to Cockcroft-Gault equation. 8. Subject has negative serum βhCG pregnancy test within 72 hours of day 1 of initial administration of vaccine in women of childbearing potential. 9. Subject does not have active infection requiring systemic therapy (In the case of such infection, it is acceptable to delay vaccine administration. The use of additional interim pembrolizumab prior to vaccine administration will be at the discretion of the treating physician).