This is a 2-part trial: a Phase 1, open-label, dose-escalation study in participants with metastatic or locally advanced solid tumors, with a consecutive Phase 2 expansion to evaluate efficacy in participants with recurrent, unresectable, or metastatic (advanced) cervical cancer that has progressed after a platinum-based treatment regimen.

Phase 1: Dose Escalation

Phase 1 will consist of a standard 3+3 dose escalation with the following escalating dose levels and schedules:

Part A1: 1, 3, and 10 milligrams/kilogram (mg/kg) administered every 2 weeks

Part A2: 6 and 10 mg/kg every 3 weeks

Each participant will stay on the dose level and schedule assigned at trial entry. Participants will receive AGEN2034 for a maximum of 2 years or until confirmed progression, unacceptable toxicity, or any criterion for stopping the study drug or withdrawal from the trial occurs.

A Safety Monitoring Committee (SMC) will assess safety; decide on dose-escalation and opening of backfill enrollment; define the recommended Phase 2 dose (RP2D); and determine opening of the Phase 2 cohorts.

In Part A1, the first participant of each cohort will be observed for 16 days (that is, ≥48 hours after second dose) for occurrence of dose-limiting toxicity (DLT) before the second participant is administered trial medication. Thereafter, within each cohort, consecutively enrolled participants may initiate treatment ≥48 hours after the prior enrolled participant-initiated treatment. Dose escalation will continue until the maximum tolerated dose (MTD) is reached or the maximum planned dose level (10.0 mg/kg) is shown to be safe. The MTD is defined as the dose below which ≥2 DLTs are observed.

Once Part A1 is completed, enrollment to Part A2 will begin. If <2 DLTs are observed in Part A1 at the maximum planned dose of 10 mg/kg every 2 weeks, open enrollment to Part A2 will begin with enrollment of 10 participants at 6 mg/kg every 3 weeks, followed by open enrollment of 10 participants at 10 mg/kg every 3 weeks. If ≥2 DLTs are observed in Part A1, at the maximum planned dose in Part A1, the standard 3+3 dose escalation will resume with Part A2 where consecutively enrolled participants in dose escalation may initiate treatment ≥48 hours after the prior enrolled participant-initiated treatment.

For cohorts in dose escalation, concurrent with the 3+3 dose escalation schema, additional participants will be backfilled to lower dose levels to ensure that each cohort enrolls a total of 10 participants. Participants enrolled to backfill cohorts may be enrolled simultaneously, without sequential dosing (that is, not required to wait 48 hours between 2 participants). These additional participants at each dose level will have the purpose of generating additional safety, pharmacokinetics, and receptor occupancy data, and will not undergo formal DLT observation.

Phase 2: Dose Expansion

To further characterize safety and efficacy, participants with recurrent, unresectable, or metastatic cervical cancer will be enrolled in Phase 2 and receive the RP2D of AGEN2034 (3 mg/kg every 2 weeks) for a maximum of 2 years or until confirmed progression, unacceptable toxicity, or any criterion for stopping the study drug or withdrawal from the trial occurs.

An SMC will assess safety, and an Independent Data Monitoring Committee will evaluate safety and efficacy.

Inclusion Criteria:

1. Voluntarily agree to participate by giving written informed consent. Participation in pharmacogenomics testing is optional.

2. Be ≥18 years of age.

3. Diagnosis and prior systemic treatment:

   1. Phase 1: Have a histologically or cytologically confirmed diagnosis of a metastatic or locally advanced solid tumor for which no standard therapy is available or standard therapy has failed.
   2. Phase 2: I. Have (1) a histologically or cytologically confirmed diagnosis of squamous-cell carcinoma, adenosquamous carcinoma, or adenocarcinoma of the cervix, and (2) metastatic, locally advanced, and/or unresectable disease at the time of enrollment. Histologic confirmation of the original primary tumor is required via pathology report. Note: The following cervical tumors are not eligible: minimal deviation/adenoma malignum, gastric type adenocarcinoma, clear cell carcinoma, and mesonephric carcinoma. II. Has cervical cancer and has relapsed after a platinum-based treatment (first line) regimen for advanced (recurrent, unresectable, or metastatic) disease; Note: Participants who have received >1 prior systemic treatment regimen for their advanced or metastatic disease will be eligible in the following cases: Participant receiving chemotherapy concurrently with primary radiation (for example, weekly cisplatin) or participant receiving adjuvant chemotherapy following completion of radiation therapy (for example, paclitaxel and carboplatin for ≤4 cycles) and progressed within 6 months after treatment completion.

4. Measurable disease - based on investigator assessment

   1. Phase 1: Have objective evidence of disease; the presence of measurable disease is not required.
   2. Phase 2: Have measurable disease on imaging based on Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST 1.1). Note: Participants must have at least one "target lesion" to be used to assess response, as defined by RECIST 1.1. Tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy. Note: Measurable disease by RECIST 1.1 must be confirmed by independent central radiologic review prior to first dose. Participants without centrally confirmed measurable disease at baseline will not be eligible for this trial.

5. Have a life expectancy of at least 3 months and an Eastern Cooperative Oncology Group performance status of 0 or 1.

6. Have adequate organ function as indicated by the following laboratory values:

   1. Adequate hematological function defined by absolute neutrophil count ≥1.5 x 10^9/liter (L), platelet count ≥100 x 10^9/L, and stable hemoglobin ≥8 grams/deciliter (without transfusions within 1 week before first dose).
   2. Adequate hepatic function based by a total bilirubin level ≤ the institutional upper limit of normal (IULN), aspartate aminotransferase level ≤2.5 x IULN, alanine aminotransferase level ≤2.5 x IULN, and alkaline phosphatase ≤2.5 x IULN.
   3. Adequate renal function defined as creatinine ≤1.5 x IULN or calculated creatinine clearance ≥50 milliliters/minute for participants with creatinine levels >1.5 x IULN (if no local guideline is available, creatinine clearance should be calculated using the Cockcroft-Gault Method).
   4. Adequate coagulation defined by international normalized ratio or prothrombin time ≤1.5 x IULN (unless the participant is receiving anticoagulant therapy); and activated partial thromboplastin time ≤1.5 x IULN (unless the participant is receiving anticoagulant therapy)

7. Other than the cancer for which the participant is enrolled, have no history of prior malignancy, with the exception of basal cell carcinoma of the skin, superficial bladder cancer, squamous-cell carcinoma of the skin, or has undergone potentially curative therapy with no evidence of that disease recurrence for 5 years since initiation of that therapy.

8. In Phase 2, participants must provide a sufficient and adequate formalin-fixed paraffin-embedded tumor tissue sample preferably from the most recent biopsy of a tumor lesion, collected either at the time of or after the diagnosis of advanced or metastatic disease has been made and from a site not previously irradiated. If no tumor tissue is available, a fresh biopsy will be required.

   Note: Tissue from needle or excisional biopsy or from resection is required.

9. Female participants must have a negative serum pregnancy test at screening (within 72 hours before first dose of study drug) if of childbearing potential or be of non-childbearing potential. Non-childbearing potential is defined as (by other than medical reasons):

   1. ≥45 years of age and has not menstruated for greater than 1 year,
   2. Amenorrheic for <2 years without a hysterectomy and oophorectomy and a follicle-stimulating hormone value in the postmenopausal range upon pretrial (screening) evaluation,
   3. Whose status is post hysterectomy, oophorectomy or tubal ligation.

10. If of childbearing potential, female participants must be willing to use 2 highly effective methods (defined in the informed consent form [ICF]) throughout the study, starting with the screening visit through 120 days after the last dose of study treatment.

    Note: Abstinence is acceptable if this is the established and preferred contraception for the participant.

11. Male participants with a female partner(s) of childbearing potential must agree to use 2 highly effective methods (defined in the ICF) throughout the trial starting with the screening visit through 120 days after the last dose of study treatment is received. Males with pregnant partners must agree to use a condom; no additional method of contraception is required for the pregnant partner.

    Note: Abstinence is acceptable if this is the established and preferred contraception for the participant.

12. Is willing and able to comply with the requirements of the protocol.

Exclusion Criteria:

1. Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigation device within 4 weeks before the first dose of treatment.

2. Has an inadequate washout period prior to first dose of study drug defined as:

   1. Received systemic cytotoxic chemotherapy or biological therapy within 3 weeks before first dose,
   2. Received radiation therapy within 3 weeks before first dose, or
   3. Had major surgery within 4 weeks before first dose.

3. Has received prior therapy with:

   1. Any antibody/drug targeting T-cell co-regulatory proteins (immune checkpoints) such as anti-PD-1, anti-programmed cell death ligand 1, or anti-cytotoxic T-lymphocyte antigen 4 (CTLA-4) antibodies
   2. For Phase 2: >1 systemic treatment regimen for the advanced (recurrent, unresectable, or metastatic) cervical cancer for which the participant is considered for the study Note: In Phase 1, prior treatment with a CTLA-4 antibody is permissible for participants with metastatic melanoma.

4. Has persisting toxicity related to prior therapy of National Cancer Institute Common Terminology Criteria for Adverse Events version 4.03 (NCI CTCAE) Grade >1 severity.

   Note: Sensory neuropathy or alopecia of Grade ≤2 is acceptable.

5. Is expected to require any other form of systemic or localized antineoplastic therapy while on trial (including maintenance therapy with another agent, radiation therapy, and/or surgical resection).

6. Has known severe hypersensitivity reactions to fully human monoclonal antibodies (NCI CTCAE Grade ≥3), any history of anaphylaxis, or uncontrolled asthma.

7. Is receiving systemic corticosteroid ≤7 days prior to the first dose of trial treatment or receiving any other form of systemic immunosuppressive medication (corticosteroid use on study for management of immune-related adverse events, and/or a premedication for IV contrast allergies/reactions is allowed). Participants who are receiving daily corticosteroid replacement therapy are an exception to this rule. Examples of permitted therapy are daily prednisone at doses of 5 to 7.5 mg or equivalent hydrocortisone dose, and steroid therapy administered by topical, intraocular, intranasal, and/or inhalation routes.

8. Has a central nervous system tumor, metastasis(es), and/or carcinomatous meningitis identified either on the baseline brain imaging obtained during the screening period or identified prior to consent. Note: Participants with history of brain metastases that have been treated may participate provided they show evidence of stable supra-tentorial lesions at screening (based on 2 sets of brain images, performed ≥4 weeks apart, and obtained after the brain metastases treatment). In addition, any neurologic symptoms that developed either as a result of the brain metastases or their treatment must have resolved or be minimal and be expected as sequelae from treated lesions. For individuals who received steroids as part of brain metastases treatment, steroids must be discontinued ≥7 days prior to first dose of study drug.

9. Has active or history of autoimmune disease that has required systemic treatment within 2 years of the start of trial treatment (that is, with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (that is, thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. Note: Participants with type 1 diabetes, vitiligo, psoriasis, hypo-, or hyperthyroid disease not requiring immunosuppressive treatment are eligible.

10. Has had an allogeneic tissue/solid organ transplant.

11. Has or had interstitial lung disease or has had a history of pneumonitis that has required oral or IV corticosteroids.

12. Has an active infection requiring intravenous systemic therapy.

13. Has known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies).

14. Has known active Hepatitis B, Hepatitis C or tuberculosis. Active Hepatitis B is defined as a known positive Hepatitis B surface antigen result. Active Hepatitis C is defined by a known positive Hepatitis C antibody result and known quantitative Hepatitis C virus ribonucleic acid results greater than the lower limits of detection of the assay.

15. Has clinically significant (that is, active) cardiovascular disease: cerebral vascular accident/stroke or myocardial infarction within 6 months before enrollment, unstable angina, congestive heart failure (New York Heart Association class ≥II), or serious uncontrolled cardiac arrhythmia requiring medication.

16. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the participant's participation for the full duration of the trial, or is not in the best interest of the participant to participate, in the opinion of the treating Investigator.

17. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.

18. Is, at the time of signing informed consent, a regular user (including "recreational use") of any illicit drugs or had a recent history (within the last year) of substance abuse (including alcohol).

19. Is legally incapacitated or has limited legal capacity.

20. Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 120 days after the last dose of study treatment.