A Study of Zalifrelimab and Balstilimab for Treatment of Participants With Metastatic or Locally Advanced Solid Tumors, and Expansion Into Select Solid Tumors (Cervical)

Inclusion Criteria To be eligible for participation in this trial the participant must: 1. Voluntarily agree to participate by giving written informed consent (participation in pharmacogenomics testing is optional). 2. Be ≥18 years of age. 3. Diagnosis: 1. Phase 1: Male or female having a histologically or cytologically confirmed diagnosis of a locally advanced, recurrent, and/or metastatic solid tumor for which no standard therapy is available or standard therapy has failed. 2. Phase 2: I. Female having (1) a histologically or cytologically confirmed diagnosis of squamous cell carcinoma, adenosquamous carcinoma, or adenocarcinoma of the cervix, and (2) locally advanced, recurrent, and/or metastatic 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 locally advanced, recurrent, and/or metastatic disease. Note: Participants who only received platinum-based chemotherapy concurrently with primary radiation (for example, weekly cisplatin) or adjuvant chemotherapy following completion of radiation therapy (for example, paclitaxel and carboplatin for ≤4 cycles) and progressed within 6 months after treatment completion will be eligible as this systemic therapy will be considered first line. 4. Measurable Disease: 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 (RECIST) version 1.1. Note: Participants must have at least one "target lesion" to be used to assess response, as defined by RECIST version 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 hemoglobin ≥8 grams/deciliter (without transfusions within 1 week of first dose). 2. Adequate hepatic function based on a total bilirubin level \<1.5 x 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 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. Note: In Phase 2, the history and time requirement for no evidence of disease for 5 years does not apply to the cancer for which the participant is enrolled in the trial. 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 locally advanced, recurrent, and/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 of 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 had menses 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 contraceptive measures (defined in the informed consent form \[ICF\]) throughout the study, starting with the screening visit through 120 days after the last dose of study drug. 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 contraceptive measures (defined in the ICF) throughout the trial starting with the screening visit through 120 days after the last dose of study drug 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 The participant must be excluded from participating in the trial if the participant: 1. Is currently participating and receiving trial therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of 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-ligand 1 of programmed cell death protein 1, or anti-CTLA-4 antibodies 2. For Phase 2: \>1 systemic treatment regimen for the locally advanced recurrent, and/or metastatic cervical cancer for which the participant is considered for the study. Participants who received a systemic regimen immediately after progressing within 6 months of completing chemotherapy concurrent with primary radiation or adjuvant chemotherapy after radiation will only be considered as having 1 prior systemic regimen for the purpose of this criterion. Note: In Phase 1, prior treatment with a CTLA-4 antibody is permissible for subjects 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 Version 4.03 Grade ≥3), any history of anaphylaxis, or uncontrolled asthma. 7. Is receiving systemic corticosteroid therapy ≤7 days prior to first dose of study 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 intravenous (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 study 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, et cetera) is not considered a form of immunosuppressive systemic treatment. Note: Participants with diabetes type 1, 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 IV 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 RNA 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 of 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 study, interfere with the participant's participation for the full duration of the study, 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 balstilimab and/or zalifrelimab.