Testing for Safety and Immune Effects of PDS0101, an Anti-HPV Therapy, Among People Living With HIV

Inclusion Criteria: * HPV 16 detected on anal swab, cervical swab or vaginal swab ≤90 days of registration. (Note: HPV 16 detected on this swab can be from the screening evaluation or through standard of care assessments. The HPV 16 assay must be FDA-cleared and report HPV 16 results separately. The assay must be performed in a CLIA-certified laboratory.) * Cervical HSIL cohort: CIN III/carcinoma in situ (CIS), CIN II/III, or CIN II with positive p16 stain diagnosed on cervical biopsy ≤90 days of registration and detection of cervical or vaginal HPV 16. * Cervical HSIL cohort: HSIL must occupy \<50% circumference of the cervical squamocolumnar junction, and adequate colposcopy with visualization of the endocervical HSIL margins. (Note: Participants with cervical HSIL occupying ≥50% of the circumference of cervical squamocolumnar junction and/or inadequate visualization of the endocervical HSIL margins are not eligible for this protocol.) * Anal HSIL cohort: anal intraepithelial neoplasia (AIN) III, AIN II/III, or AIN II with positive p16 stain diagnosed on anal or perianal biopsy ≤90 days of registration and detection of anal HPV 16. * Anal HSIL cohort: HSIL must occupy \<50% circumference of the squamocolumnar junction. (Note: Participants with anal HSIL occupying ≥50% of the circumference of cervical squamocolumnar junction are not eligible for this protocol.) * Ages 25-65 years (i.e., no longer eligible on the 66th birthday). * HIV infection with receipt of antiretroviral therapy for at least 12 months. * CD4+ T-cell count ≥200 cells/mm3 ≤45 days of registration. * Plasma HIV-1 RNA \<200 copies/mL ≤45 days of registration. * Participants must meet the following laboratory parameters ≤45 days before enrollment: 1. Absolute neutrophil count: ≥1,500/mm3 2. Platelets: ≥100,000/mm3 3. Hemoglobin \>12.5 g/dL for men and \>11.5 g/dL for women 4. Estimated glomerular filtration rate (eGFR) \>70 mL/min/1.73m2 using the Chronic Kidney Disease Epidemiology Collaboration (CKD-Epi) equation or serum creatinine \<1.2 x upper limit of normal (ULN) 5. Aspartate aminotransferase (AST) (SGOT), and alanine aminotransferase (ALT) (SGPT), \<1.5 x ULN 6. Total bilirubin \<1.5 x ULN * Eastern Cooperative Oncology Group (ECOG) performance status ≤1 (or Karnofsky ≥70%). * Willingness to comply with three-dose immunotherapeutic agent schedule and subsequent study visits. * The effects of PDS0101 on the developing human fetus at the recommended therapeutic dose are unknown. For this reason, women of child-bearing potential (WOCBP) and men must agree to use adequate contraception prior to study entry and for at least 120 days after the last dose of study treatment. Women of childbearing potential must have a negative urine pregnancy test (β-human chorionic gonadotropin) within 24 hours prior to registration and prior to visits on Days 1, 22, 43, 57, and 127. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her study physician immediately and will not receive any additional doses of immunotherapeutic agent. Women who become pregnant and partners of male participants who become pregnant will be followed to assess pregnancy outcomes. * Ability to understand and the willingness to sign a written informed consent form (ICF). Exclusion Criteria: * AIDS-defining condition within 6 months prior to study entry. * Receipt of blood products within 6 months of enrollment or are currently taking immune suppressants. * History of HPV-related cancer or suspected cancer of the cervix, anus, vagina, vulva, penis, or oropharynx. * Current diagnosis of cancer or prior invasive cancer \> T1 stage (other than non-melanoma skin cancer) that has required active treatment within the past 3 years. * Suspicion of invasive cancer of the cervix, vulva, vagina, perianus or anal canal. (Note: Concomitant vulvar, vaginal, or perianal HSIL is not exclusionary.) * Surgical or ablative treatment for anal or cervical HSIL within 180 days of study entry. * Prior receipt of any doses of a licensed or experimental HPV immunotherapeutic agent. (Note: Prior receipt of licensed prophylactic HPV vaccines is permitted.) * Planned use of intravaginal, vulvar, perianal or intra-anal imiquimod or 5-fluorouracil or another topical therapeutic agent with possible activity against HPV disease, or their use within ≤90 days of entry. * Receipt of a live vaccine within 30 days prior to the first dose of treatment. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist®) are live attenuated vaccines and are not allowed. Coordination and timing of COVID-19 vaccination should be based on local Investigator clinical assessment and judgment. * Received immunotherapy/immunomodulatory or immunosuppressive agents (e.g., IFNs, tumor necrosis factor, interleukins, immunoglobulins or other biological response modifiers \[GM-CSF, granulocyte-macrophage colony-stimulating factor\]) within 6 weeks prior to administration of the first study treatment. * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 30 days prior to the first dose of study treatment. (Note: Participants who entered the follow-up phase of an investigational study may participate as long as it has been 30 days after the last dose of the previous investigational agent.) * Is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. Current or recent use of intra-articular, topical, or inhaled corticosteroids is acceptable. * Participants known to be positive for Hepatitis B antigen (HBsAg)/Hepatitis B virus (HBV) DNA or active Hepatitis C. Active Hepatitis C (HCV) is defined by a known positive HCV antibody result and known quantitative HCV RNA results greater than the lower limits of detection of the assay. * Plan to relocate during study period. * Acute medical conditions that would require exclusion from participation based on the opinion of the supervising physician. * Potential participants receiving any other investigational agents may be excluded in the opinion of the supervising physician. * Use of opioids within 2 weeks prior to enrollment. (Note: Medically assisted therapy for opioid use disorder or alcohol use disorder (e.g., stable methadone or buprenorphine/naloxone) are not exclusionary. The rationale for excluding other opioid use is to allow appropriate grading of injection-related pain.) * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Current bacterial sexually transmitted infection (STI) requiring treatment (participants may participate after adequate treatment, at the discretion of the treating provider). * Pregnant or breastfeeding, unwilling/unable to use contraception, or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of any study treatment. a) For the purpose of this study, a WOCBP (i.e., fertile) is defined as the period following menarche and until becoming post-menopausal unless permanently sterile. Acceptable methods of birth control for this study include: i) Permanent sterilization methods include hysterectomy, bilateral salpingectomy and bilateral oophorectomy. ii) A post-menopausal state is defined as no menses for 12 months without an alternative medical cause. A high follicle stimulating hormone (FSH) level in the post-menopausal range may be used to confirm a post-menopausal state in women not using hormonal contraception or hormonal replacement therapy. However, in the absence of 12 months of amenorrhea, a single FSH measurement is insufficient. iii) Use of a barrier (diaphragm or condom) with spermicide iv) Combined hormonal (estrogen and progestogen) contraception associated with inhibition of ovulation v) An intrauterine device/system vi. An oral, transdermal, or injectable contraceptive vii. A vasectomized partner is a highly effective birth control method provided that partner is the sole sexual partner of the WOCBP trial participant and that the vasectomized partner has received medical assessment of the surgical success. b) For the purpose of this study, a man is considered fertile after puberty unless permanently sterile by bilateral orchidectomy. i. Male participants must agree to use a condom as an effective method of contraception throughout the study and for at least 120 days after the last dose of study treatment. * Use of anticoagulants other than non-steroidal anti-inflammatory drugs or aspirin.