A Phase 1 Study in Patients With HPV16+ Recurrent/ Metastatic Head and Neck Squamous Cell Carcinoma

General: 1. Ability to provide informed consent and documentation of informed consent prior to initiation of any study-related tests or procedures that are not part of standard of care for the patient's disease. Patients must also be willing and able to comply with study procedures, including the acquisition of specified research specimens 2. Age ≥18 years old 3. ECOG performance status of 0 or 1 4. Life expectancy ≥12 weeks 5. Measurable disease as per RECIST 1.1 and documented by CT and/or MRI. Cutaneous or subcutaneous lesions must be measurable by calipers. Note: Lesions to be used as measurable disease for the purpose of response assessment must either a) not reside in a field that has been subjected to prior radiotherapy, or b) have demonstrated clear evidence of radiographic progression since the completion of prior radiotherapy and prior to study enrollment 6. R/M HNSCC that has progressed following at least 1 prior systemic therapy. Patients must have received platinum-based chemotherapy and/or pembrolizumab in the first-line setting 7. Patient must have HLA A\*0201 genotype as determined by genomic testing performed at a central laboratory designated by the Sponsor. 8. Patient must have histologically and/or cytologically proven tumor(s) that are HPV16+ and express 16INK4A. Archival tissue or FFPE tissue from a biopsy and/or surgery must be available for HPV16 and p16INK4A testing on all patients enrolled. All tumors must test positive for both HPV16 using RNA ISH and p16INK4A expression in tumor cells using IHC analysis determined in a central laboratory designated by the Sponsor. All tumors must have histologically or cytologically confirmed diagnoses. Laboratory Features 9. Acceptable laboratory parameters as follows: 1. Platelet count ≥100 x 103/µL 2. Hemoglobin ≥9.0 g/dL. Criteria must be met without erythropoietin dependency and without pRBC transfusion within last 2 weeks. 3. Absolute neutrophil count ≥1.5 × 103/µL in the absence of any growth factor support within 2 wks prior to the initiation of study drug 4. ALT or AST ≤3.0 × ULN; for patients with hepatic metastases, ALT and AST ≤5 × ULN 5. Total bilirubin ≤1.5 × ULN, except patients with Gilbert's syndrome, who may enroll if the conjugated bilirubin (total and direct) is within normal limits 6. Creatinine \<1.5 mg/dL, or a calculated or measured creatinine clearance \>30 mL/min 7. Coag: INR or PT ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within the therapeutic range of anticoagulants. Reproductive Features 10. Female patients of childbearing potential (not surgically sterilized and between menarche and 1 year post-menopause) must have a negative serum pregnancy test performed within 72 hours prior to the initiation of study drug administration. Further, female patients of childbearing potential must agree to use acceptable contraceptive measures from the time of main study consent through 30 days after discontinuation of study drug administration. For female patients, 2 forms of contraception must be utilized and may include oral, transdermal, injectable, or implantable contraceptives; intrauterine device; female condom; diaphragm with spermicide; cervical cap; or use of a condom by the sexual partner or a sterile or vasectomized sexual partner. Periodic abstinence (eg, calendar, ovulation, symptothermal, and post ovulation methods) and withdrawal are not considered acceptable forms of contraception in this study. 11. Non-vasectomized male patients with partners of childbearing potential must use barrier contraception. In addition, male patients should also have their partners use another method of contraception from the time of main study consent through 30 days after discontinuation of study drug administration. 12. Female patients should not be pregnant or plan to become pregnant during the course of the trial. 13. Female patients must not be breastfeeding. Previous Checkpoint Inhibitor (CI) Therapy 14. Patients who have previously received an immune CI (eg, anti-PD L1, anti-PD 1, anti-cytotoxic T lymphocyte-associated antigen 4 \[CTLA-4\]) prior to enrollment must have toxicities related to the CI resolved to ≤Grade 1 or baseline (prior to the CI) to be eligible for enrollment. Note that patients who experienced previous hypothyroidism toxicity on a CI are eligible to enter study regardless of CTCAE grade resolution as long as the patient is well controlled on thyroid replacement hormone. Exclusion Criteria 1. Patients with symptomatic CNS metastases must have been treated, be asymptomatic, and not have any of the following at the time of enrollment: 1. Need for concurrent treatment for the CNS disease (eg, surgery, radiation, corticosteroids \>10 mg prednisone/day or equivalent); 2. Progression of CNS metastases on MRI or CT for at least 28 days after last day of prior therapy for the CNS metastases; and/or 3. Concurrent leptomeningeal disease or cord compression. 2. Has an active autoimmune disease that has required systemic treatment in past 2 years (ie, with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed. 3. History of prior allogeneic bone marrow, stem-cell or solid organ transplantation 4. Treatment with any systemic anti-neoplastic therapy, or investigational therapy within the 2 weeks (or 4 weeks, for antibody drugs), prior to the initiation of study drug administration. Patients may be on an investigational or other anti-neoplastic therapy during the screening phase of the study. 5. Treatment with radiation therapy within 2 weeks prior to the initiation of study drug administration. 6. Treatment with corticosteroids (\>10 mg per day prednisone or equivalent) or other immune suppressive drugs within the 14 days prior to the initiation of study drug administration. 7. History of clinically significant cardiovascular disease including, but not limited to: 1. Myocardial infarction or unstable angina within the 16 weeks prior to the initiation of study drug 2. Clinically significant cardiac arrhythmias 3. Uncontrolled HTN: systolic BP \>180 mm Hg, diastolic BP \>100 mm Hg 4. Deep vein thrombosis, pulmonary embolism, stroke, or transient ischemic attack within the 16 weeks prior to the initiation of study drug 5. QTcB prolongation \>480 msec 6. CHF (NY Heart Association Class III IV) 7. Pericarditis/clinically significant pericardial effusion 8. Myocarditis 8. Clinically significant pulmonary compromise (eg, requirement for supplemental oxygen) 9. Clinically significant GI disorders including: 1. History of GI perforation within 1 year prior to study drug administration. Patients with a history of GI perforation that occurred more than 1 year ago can only be enrolled if the Investigator no longer considers the previously affected area to be at risk for perforation; 2. History of clinically significant GI bleeding within 3 months prior to the initiation of study drug 3. History of acute pancreatitis within 3 months prior to the initiation of study drug; and/or 4. Diverticulitis that is clinically significant in the opinion of the investigator based on the extent or severity of known disease and/or the occurrence of clinically significant disease flares within 4 weeks prior to the initiation of study drug administration. 10. Patients who experienced the following immune checkpoint inhibitor-related AEs are ineligible even if the AE resolved to ≤Grade 1 or baseline: 1. ≥Grade 3 ocular AE 2. Changes in liver function tests that met the criteria for Hy's Law (\>3 × ULN of either ALT/AST with concurrent \>2 × ULN of total bilirubin (total and direct) and without alternate etiology) 3. ≥Grade 3 neurologic toxicity 4. ≥Grade 3 colitis 5. ≥Grade 3 renal toxicity 11. Evidence of active viral, bacterial, or systemic fungal infection requiring parenteral treatment within 7 days prior to the initiation of study drug. Patients requiring any systemic antiviral, antifungal, or antibacterial therapy for active infection must have completed treatment no less than 1 week prior to the initiation of study drug. 12. Known positive testing for human immunodeficiency virus or history of acquired immune deficiency syndrome. 13. Known history of hepatitis B or hepatitis C infection or known positive test for hepatitis B surface antigen, hepatitis B core antigen, or hepatitis C polymerase chain reaction. 14. Second primary invasive malignancy that has not been in remission for \>2 years. Exceptions that do not require a 2 year remission include: non-melanoma skin cancer; cervical carcinoma in situ on biopsy; squamous intraepithelial lesion on Pap smear; localized prostate cancer (Gleason score \<6); or resected melanoma in situ. 15. History of trauma or major surgery within 4 weeks prior to the initiation of study drug administration. 16. Any serious underlying medical or psychiatric condition that would impair the ability of the patient to receive or tolerate the planned treatment at the investigational site. 17. Known hypersensitivity to recombinant proteins, polysorbate 80 or any excipient contained in the drug formulation for CUE 101. 18. Vaccination with any live virus vaccine within 4 weeks prior to the initiation of study drug administration. Inactivated annual influenza vaccination is allowed. 19. Dementia or altered mental status that would preclude understanding and rendering of informed consent. 20. Active or history of alcohol or other substance abuse within 1 year prior to the initiation of study drug administration. 21. Any investigative site personnel directly affiliated with this study. 22. Prisoners or other individuals who are involuntarily detained. 23. Any issue that would contraindicate the patient's participation in the study or confound the results of the study. Parts C and D The patient population to be enrolled will consist of R/M HLA-A\*0201-positive adult patients with HPV-driven HNSCC, as confirmed by tumor HPV16 positivity, expression of p16INK4A and tumor expression of PD L1 (CPS ≥1) as determined by an FDA-approved test, eg, the PD L1 IHC 22C3 pharmDx kit approved for use as a companion diagnostic device. Inclusion Criteria General: 1. Ability to provide informed consent and documentation of informed consent prior to initiation of any study-related tests or procedures that are not part of standard of care for the patient's disease. Patients must also be willing and able to comply with study procedures, including the acquisition of specified research specimens. 2. Age ≥18 years old 3. ECOG performance status of 0 or 1 4. Life expectancy ≥12 weeks 5. Measurable disease as per RECIST 1.1 and documented by CT and/or MRI by the local site investigator/radiology. At least 1 lesion that can be accurately measured in at least 2 dimensions with spiral CT scan. Minimum measurement must be \>15 mm in the longest diameter by \>10 mm in the short axis. Cutaneous or subcutaneous lesions must be measurable by calipers. Note: Lesions to be used as measurable disease for the purpose of response assessment must either a) not reside in a field that has been subjected to prior radiotherapy, or b) have demonstrated clear evidence of radiographic progression since the completion of prior radiotherapy and prior to study enrollment. 6. All tumors must have histologically or cytologically confirmed diagnoses of recurrent and/or metastatic HNSCC. 7. Patient must have HLA A\*0201 genotype as determined by genomic testing performed at a central laboratory designated by the Sponsor prior to enrollment. 8. Patient must have tumor(s) that are HPV16+ and express 16INK4A. Archival tissue or FFPE tissue from a biopsy and/or surgery must be available for HPV16 and p16INK4A testing on all patients enrolled. All tumors must test positive for both HPV16 using RNA ISH and p16INK4A expression in tumor cells using IHC analysis determined in a central laboratory designated by the Sponsor. 9. Patient must have tumor expression of PD L1 (CPS ≥1) as determined by an FDA-approved test. Laboratory Features 10. Acceptable laboratory parameters as follows: 1. Platelet count ≥100 × 103/μL 2. Hemoglobin ≥9.0 g/dL. Criteria must be met without erythropoietin dependency and without pRBC transfusion within last 2 weeks. 3. Absolute neutrophil count ≥1.5 × 103/μL in the absence of any growth factor support within 2 weeks prior to the initiation of study drug 4. ALT or AST ≤2.5 × ULN; for patients with hepatic metastases, ALT and AST ≤5 × ULN 5. Total bilirubin ≤1.5 × ULN, except patients with Gilbert's syndrome, who may enroll if the conjugated bilirubin (total and direct) is within normal limits 6. Creatinine ≤1.5 mg/dL, or a calculated or measured creatinine clearance ≥30 mL/min. Creatinine clearance should be calculated as per institutional standard. \>1.5 x institutional ULN. Glomerular filtration rate (GFR) can also be used in place of creatinine or creatinine clearance. 7. Coagulation: INR or PT ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within the therapeutic range of anticoagulants. Reproductive Features 11. A male participant must agree to use contraception during the treatment period and for at least 120 days following discontinuation of study treatment. 12. A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least 1 of the following conditions applies: 1. Not a woman of childbearing potential (WOCBP) 2. A WOCBP who agrees to follow contraceptive guidance during the treatment period and for at least 120 days after the last dose of study treatment. Exclusion Criteria 1. Patients who have received prior therapy for R/M disease. 2. Patients with symptomatic CNS metastases must have been treated, be asymptomatic, and not have any of the following at the time of enrollment: 1. Need for concurrent treatment for the CNS disease (eg, surgery, radiation, corticosteroids \>10 mg prednisone/day or equivalent); 2. Progression of CNS metastases on MRI or CT for at least 28 days after last day of prior therapy for the CNS metastases. If brain imaging is performed to document the stability of existing metastases, MRI should be used if possible. If MRI is medically contraindicated, CT with contrast is an acceptable alternative. 3. and/or concurrent leptomeningeal disease or cord compression. 3. Has an active autoimmune disease that has required systemic treatment in past 2 years (ie, with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed. 4. History of prior allogeneic bone marrow, stem-cell or solid organ transplantation 5. Treatment with prior systemic anti-cancer therapy including investigational agents within 4 weeks for antibodies or 5 half-lives for other therapies, whichever is shorter, prior to administration of the study drug. Patients may be on an investigational or other anti-neoplastic therapy during the screening phase of the study. 6. Treatment with radiation therapy within 2 weeks prior to the initiation of study drug administration. 7. Treatment with corticosteroids (\>10 mg per day prednisone or equivalent) or other immune suppressive drugs within the 14 days prior to the initiation of study drug administration. 8. History of clinically significant cardiovascular disease including, but not limited to: 1. Myocardial infarction or unstable angina within the 16 weeks prior to the initiation of study drug 2. Clinically significant cardiac arrhythmias 3. Uncontrolled HTN: systolic BP \>180 mm Hg, diastolic BP \>100 mm Hg 4. Deep vein thrombosis, pulmonary embolism, stroke, or transient ischemic attack within the 16 weeks prior to the initiation of study drug 5. QTcB prolongation \>480 msec 6. CHF (NY Heart Association Class III-IV) 7. Pericarditis/clinically significant pericardial effusion 8. Myocarditis 9. Clinically significant pulmonary compromise (eg, requirement for supplemental oxygen) 10. Clinically significant GI disorders including: 1. History of GI perforation within 1 year prior to study drug administration. Patients with a history of GI perforation that occurred more than 1 year ago can only be enrolled if the Investigator no longer considers the previously affected area to be at risk for perforation; 2. History of clinically significant GI bleeding within 3 months prior to the initiation of study drug; 3. History of acute pancreatitis within 3 months prior to the initiation of study drug; and/or 4. Diverticulitis that is clinically significant in the opinion of the investigator based on the extent or severity of known disease and/or the occurrence of clinically significant disease flares within 4 weeks prior to the initiation of study drug administration. 11. Severe hypersensitivity to pembrolizumab excipients. 12. Evidence of active viral, bacterial, or systemic fungal infection requiring parenteral treatment within 7 days prior to the initiation of study drug. Patients requiring any systemic antiviral, antifungal, or antibacterial therapy for active infection must have completed treatment no less than 1 week prior to the initiation of study drug. 13. Known positive testing for human immunodeficiency virus or history of acquired immune deficiency syndrome. 14. Known history of hepatitis B or hepatitis C infection or known positive test for hepatitis B surface antigen, hepatitis B core antigen, or hepatitis C polymerase chain reaction. 15. Second primary invasive malignancy that has not been in remission for \>2 years. Exceptions that do not require a 2 year remission include: non-melanoma skin cancer; cervical carcinoma in situ on biopsy; squamous intraepithelial lesion on Pap smear; localized prostate cancer (Gleason score \<6); or resected melanoma in situ. 16. History of trauma or major surgery within 4 weeks prior to the initiation of study drug administration. 17. Any serious underlying medical or psychiatric condition that would impair the ability of the patient to receive or tolerate the planned treatment at the investigational site. 18. History of (non-infectious) pneumonitis that required steroids or has current pneumonitis. 19. Known hypersensitivity to recombinant proteins, polysorbate 80 or any excipient contained in the drug formulation for CUE 101. 20. Vaccination with any live virus vaccine within 4 weeks prior to the initiation of study drug administration. Inactivated annual influenza vaccination is allowed. 21. Dementia or altered mental status that would preclude understanding and rendering of informed consent. 22. Active or history of alcohol or other substance abuse within 3 months prior to the initiation of study drug administration. Medical marijuana use is not allowed on study. 23. Any investigative site personnel directly affiliated with this study. 24. Prisoners or other individuals who are involuntarily detained. 25. Any issue that would contraindicate the patient's participation in the study or confound the results of the study.