The goal of this clinical trial is to determine the maximum tolerated dose and to find out the side effects of a drug called IBRX-042 at different dose levels in patients with recurrent or progressive Human Papillomavirus (HPV) associated tumors. The main questions it aims to answer are:

• What is the maximum tolerated dose of IBRX-042?
• How well does the study drug treat cancer?
• What effects the study drug may have on the human body and cancer?

Participants will receive IBRX-042 at one of three dose levels every 3 weeks for a total of 3 injections. Participants will undergo tests, exams, and procedures that are part of standard of care and for study purposes. IBRX-042 will be administered by injection every 3 weeks for a total of 3 injections.

Up to 60 participants may be screened for up to 18 participants to receive at least 1 dose of study treatment. Participants will be administered IBRX-042 by injection once every 3 weeks for a total of 3 injections.

Participants will receive study treatments until they report progressive disease (PD), unacceptable toxicity, withdraw consent, or if the Investigator feels it is no longer in their best interest to continue treatment.

Participants who progress, discontinue treatment, or complete the study will attend an end-of- treatment (EOT) visit 30 (± 5) days after the last administration of study treatment.

Additionally, participants will attend a follow-up visit 6 months following administration of the last dose of IBRX-042. After the participants completes or withdraws from the study, the study team will contact participants approximately every 3 months for a minimum of 1 year post administration of the first dose of study drug and then yearly until death to collect follow-up information, including survival status, collection of adverse events, and any current cancer treatment regimen. A clinic visit will be scheduled for 6 months after the last injection administered for collection of whole blood for exploratory immune and molecular profiling.

Inclusion Criteria:

1. 18-75 years of age.

2. Able to understand and provide a signed informed consent that fulfills the relevant Institutional Review Board (IRB) or Independent Ethics Committee (IEC) guidelines.

3. Histologically confirmed HPV-associated cancer documented as HPV- or p16-positive carcinoma (measurable or non-measurable disease).

4. Participants must have received at least 1 standard of care therapy per National Comprehensive Cancer Network (NCCN) guidelines for their HPV-associated cancer > 28 days prior to enrollment.

5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.

6. Resolution of all toxic side effects of prior therapy for their HPV-associated cancer to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) Version 5 grade ≤ 1.

7. Ability to attend required study visits and return for adequate follow-up, as required by this protocol.

8. Agreement to practice effective contraception for female participants of child-bearing potential and nonsterile males. Female participants of child-bearing potential must agree to use effective contraception for up to 30 days after last dose of study treatment. Nonsterile male participants must agree to use a condom while on study and for up to 30 days after the last dose of study treatment. Effective contraception includes surgical sterilization (eg, vasectomy, tubal ligation), two forms of barrier methods (eg, condom, diaphragm) used with spermicide, and intrauterine devices (IUDs).

9. Adequate organ function, evidenced by the following laboratory results:

   1. Absolute neutrophil count (ANC) ≥ 1.5 x 109/L
   2. Absolute lymphocyte count (ALC) > institutional lower limit of normal
   3. Hemoglobin ≥ 10.0 g/dL.
   4. Platelet count ≥ 100 × 109/L
   5. Total bilirubin ≤ 1.5 × upper limit of normal (ULN; unless the participant has documented Gilbert's syndrome).
   6. Aspartate aminotransferase [serum glutamic-oxaloacetic transaminase] (AST [SGOT]) or alanine aminotransferase [serum glutamic-pyruvic transaminase] (ALT [SGPT]) ≤ 3.0 × ULN. For patients with significant hepatic involvement by tumor, ALT ≤ 5 × ULN is acceptable.
   7. Albumin ≥ 3.0 g/dL. Note: Each study site should use its institutional ULN to determine eligibility.

Exclusion Criteria:

1. Serious uncontrolled concomitant disease that would contraindicate the use of the investigational drugs used in this study or that would put the participant at high risk for treatment-related complications.
2. Serious pulmonary disease.
3. Active hepatitis.
4. Positive results of screening test for hepatitis B virus and/or hepatitis C virus.
5. 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 participants who have known contrast allergies is allowed.
6. Participants taking any medication(s) (herbal or prescribed) known to have an adverse drug reaction with any of the study medications.
7. Participation in an investigational drug study or receiving any investigational treatment within 28 days prior to study treatment. Approved drugs for the prevention and treatment of COVID-19 are permitted.
8. Concurrent participation in any interventional clinical trial.
9. Assessed by the Investigator to be unable or unwilling to comply with the requirements of the protocol.
10. Pregnant and nursing women.