Inclusion Criteria:
* At least 18 years of age
* Eastern Cooperative Oncology Group (ECOG) ≤ 2 or Karnofsky Performance Status of ≥ 60
* Participants must have recurrent, persistent, or metastatic cervical cancer, including squamous cell, adenocarcinoma, and adenosquamous histologies recurrent, persistent, or metastatic p16+ cell cancer of the vagina or vulva
* Measurable disease per irRECIST
* Previously irradiated lesions can be considered as measurable disease only if progressive disease has been unequivocally documented at that site since radiation
* Measurable lesions are defined as those that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥10 mm (≥1 cm) with computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam.
* Must have at least 2 distinct lesions as documented by imaging studies within 4 weeks prior to randomization
* Consent to biopsy of metastatic site or consent to retrieval of archival tissue
Exclusion Criteria:
* Patients with known brain metastasis
* Active autoimmune disease or immune deficiency, including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, autoimmune thyroid disease, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjögren's syndrome, Guillain-Barré syndrome, or multiple sclerosis with the following exceptions:
* Patients with a history of autoimmune-related hypothyroidism who are on thyroid-replacement hormone are eligible for the study
* Patients with controlled type 1 diabetes mellitus who are on an insulin regimen are eligible for the study
* History of prior malignancy within 2 years prior to screening, with the exception of those with a negligible risk of metastasis or death (e.g., 5-year OS of \> 90%), such as but not limited to, non-melanoma skin carcinoma, ductal carcinoma in situ, or stage I endometrioid uterine cancer, and others at the discretion of the Principal Investigator (PI)
* Treatment with systemic immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor (TNF)-α agents) within 2 weeks prior to initiation of study treatment, or anticipation of need for systemic immunosuppressive medication during the course of the study, with the following exceptions:
* Patients who received acute, low-dose systemic immunosuppressant medication or a one-time pulse dose of systemic immunosuppressant medication (e.g., 48 hours of corticosteroids for a contrast allergy)
* Patients who received mineralocorticoids (e.g., fludrocortisone), corticosteroids for chronic obstructive pulmonary disease or asthma, or low-dose corticosteroids for orthostatic hypotension or adrenal insufficiency
