pBI-11 & TA-HPV (With Pembrolizumab as Treatment for Patients w/Advanced, PD-L1 CPS≥1, hrHPV+ Oropharyngeal Cancer

Disease that can be treated with curative intent as assessed by patient's study physician. If patient in this situation wishes for treatment with palliative intent then they may enroll

Multiple primary oropharyngeal (OP) tumors

Primary cancer not originated from the oropharynx

Has received any therapy for R/M disease. Therapy in the setting of curative intent is allowed

Patient is pregnant or breastfeeding

Prior prophylactic or therapeutic vaccination with any human papillomavirus (HPV) antigen except L1

\* Note: previous receipt of the Gardasil (registered trademark) vaccine (including Gardasil 9 \[registered trademark\]) or the Cervarix (registered trademark) vaccine does not exclude

Has received a live vaccine within 30 days prior to first dose of study treatment

* Examples of prohibited live vaccines include, but are not limited to measles, mumps, rubella, varicella (chickenpox), zoster (shingles; Zostavax \[registered trademark\] \[not including Shingrix (registered trademark)\]), yellow fever, rabies, bacillus Calmette-Guerin (BCG), and typhoid (oral) vaccine

* Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist \[registered trademark\] Quadrivalent) are live attenuated vaccines and are not allowed. The three United States (US) FDA-approved coronavirus disease 2019 (COVID-19) vaccines (by Pfizer BioNTech, Moderna, and Janssen) and AstraZeneca COVID-19 vaccine are based on messenger (m)RNA or replication-deficient adenoviral vectors and are allowed

Is currently participating in or, within 4 weeks prior to first dose of study treatment, has participated in a study of an investigational agent or has used an investigational device

* Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent

* Patients with persistent toxicities of =\< grade 3 (National Cancer Institute \[NCI\]-Common Terminology Criteria for Adverse Events \[CTCAE\] v5.0) will be excluded

Diagnosis of immunodeficiency

Known additional malignancy that is non-localized or progressing or has required active treatment within the past 3 years prior to first dose of study treatment

\* Note: Participants with usual basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (for example, in situ cervical cancer or breast carcinoma, superficial bladder cancer, or non-invasive intraductal carcinoma of the prostate) that have undergone potentially curative therapy are not excluded

Radiographically detectable (even if asymptomatic and/or previously treated) central nervous system metastases and/or carcinomatous meningitis as assessed by local site investigator and radiology review

Recipient of previous allogeneic tissue/solid organ transplant

Known severe hypersensitivity (\>= grade 3) to pembrolizumab and/or any of its excipients

History of myocarditis or pericarditis or other known clinically significant underlying heart disease (e.g., cardiomyopathy, congestive heart failure, symptomatic arrhythmia not controlled by medication, unstable angina, history of acute myocardial infarction)

Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, sepsis, or psychiatric illness/social situations that would limit compliance with study requirements

Active or chronic infection with any of the following (with testing for all three conditions required during screening for this study):

* Human immunodeficiency virus (HIV)

* Hepatitis C virus (HCV)

* Hepatitis B virus (HBV)

Active autoimmune disease with immunodeficiency as a clinical component (e.g., rheumatoid arthritis, systemic lupus erythematosus \[SLE\], ulcerative colitis, Crohn's disease, multiple sclerosis \[MS\], ankylosing spondylitis)

Within 60 days prior to initiating first dose of protocol-indicated treatment, patient has received therapy with immunosuppressive drugs such as cyclosporine, adrenocorticotropic hormone (ACTH), alkylating agents, antimetabolites, radiation, tumor necrosis factor (TNF) inhibitors, or systemic corticosteroids

Recognized immunodeficiency diseases including cellular immunodeficiencies; hypo-gammaglobulinemia or dys-gammaglobulinemia; or acquired, hereditary, or congenital immunodeficiencies

Patients and their close social, sexual, or domestic contacts may not have non-healed wounds or active exfoliative skin conditions, such as eczema, burns, impetigo, varicella-zoster virus infection, herpes simplex virus infection, severe acne, severe diaper dermatitis with extensive areas of denuded skin, psoriasis, lichen planus, or Darier disease (keratosis follicularis)

History and presence of atopic dermatitis

Patients and their close social, sexual, or domestic contacts may not have known conditions associated with immunosuppression, such as HIV/acquired immunodeficiency syndrome (AIDS), leukemia, lymphoma, generalized malignancy, solid organ transplant recipient, or hematopoietic stem cell transplant recipient \< 24 months post-transplant OR \>= 24 months, but who have graft-versus-host disease or disease relapse, or be of less than 1 year of age

Found at screening visit to have severe arrhythmias (e.g., atrial fibrillations), sinus bradycardia (\< 50 beats per minute \[BPM\]), sinus tachycardia (\> 100 BPM) via resting electrocardiography (EKG). Patients with controlled arrhythmias followed by a cardiologist are eligible

Patients with active interstitial lung disease (ILD)/pneumonitis or a history of ILD/pneumonitis requiring treatment with systemic steroids. Hypoxemia (oxygen saturation \[SpO2\] \< 92% for 5 min or longer) by finger pulse oximetry corrected by oxygen supplementation is allowed

What this study is about