Dostarlimab and Cobolimab in Advanced Cervical Cancer

Inclusion Criteria Cohorts A \& B: * Participants must have histologically or cytologically confirmed cervical carcinoma, all histologies included. * All patients must have measurable disease as defined by RECIST 1.1. as defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded). Each lesion must be \>10 mm when measured by CT, MRI or caliper measurement by clinical exam; or \>20 mm when measured by chest x-ray. Lymph nodes must be \>15 mm in the short axis when measured by CT or MRI. Radiological evaluation should occur within 30 days prior to enrollment initiation. * Age of 18 or greater years. Because insufficient dosing or adverse event data are available on the use of dostarlimab or cobolimab in participants \<18 years of age, children are excluded from the study. Cervical cancer is rare in the pediatric population. * ECOG performance status 0, 1, or 2. * Availability of at least two formalin fixed paraffin embedded (FFPE) blocks of cancer tissue OR at least 1 FFPE block AND at least 3 unstained 5-micron slides, OR at least 1 unstained 5-micron slides from original surgery or biopsy or from a biopsy of recurrent disease. * Participants must have adequate organ and marrow function as defined below: * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * hemoglobin ≥ 9 g/dL * total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) OR direct bilirubin ≤ 1.0 x ULN * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional ULN unless liver metastases are present, in which case they must be ≤ 5.0 x ULN * creatinine ≤ 1.5 x institutional ULN OR Glomerular filtration rate (GFR) ≥50 mL/min/1.73 m2 unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m2 (see Appendix B). * INR or PT ≤ 1.5 x ULN unless the patient receives anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants. * aPTT ≤ 1.5 x ULN unless patient is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants. * Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured (via sustained virologic response). For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Participants with treated brain metastases are eligible if follow-up brain imaging at least 4 weeks after central nervous system (CNS)-directed therapy shows no evidence of progression. * Participants must not be pregnant or breastfeeding given that dostarlimab and cobolimab have unknown effects in pregnancy and breastfeeding and the potential for teratogenesis. Females of childbearing potential are defined as those who are not surgically sterile (i.e., Bilateral tubal ligation, bilateral oophorectomy or complete hysterectomy) or post-menopausal (defined as \>= 12 months with no menses without an alternative medical cause). Serum pregnancy test (for females of childbearing potential) must be negative at screening (within 72 hours of initiating study treatment). * The effects of dostarlimab and cobolimab on the developing human fetus are unknown. For this reason and because immunomodulatory agents are known to be teratogenic, women of child-bearing potential must agree to use a highly effective contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation and at least 250 days after last treatment administration dostarlimab and cobolimab. Male partners of a woman participating in the study also need to agree to contraception for at least 160 days after the last treatment administration of dostarlimab and cobolimab. Should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately. * Toxicities of prior therapy (excepting alopecia and sensory neuropathy) should be resolved to ≤ grade 1 per the revised NCI Common Terminology Criteria for Adverse Events (CTCAE) version 5. * Ability to understand and the willingness to sign a written informed consent document. Inclusion Criteria Specific to Cohort A: -Prior therapy: * Patients must have received platinum-based therapy; any platinum-based chemotherapy (single agent or any platinum doublet) administered in conjunction with primary radiation will be counted as a prior regimen. * Patients must NOT have received any class of drugs targeted to the PD-1/PD-L1 pathway * Patients must NOT have received any class of drugs targeting TIM3 pathway Inclusion Criteria Specific to Cohort B: * PD-L1 CPS ≥ 1% by IHC * Prior therapy: * Patients must have received prior platinum-based therapy. Any platinum-based chemotherapy (single agent or any platinum doublet) administered in conjunction with primary radiation will be counted as a prior regimen. * Patients may have received prior pembrolizumab either as first line therapy in combination with platinum-based chemotherapy with or without bevacizumab and did not progress in the 18 weeks of therapy OR patients who received pembrolizumab as a subsequent line of therapy who did not progress in the first 18 weeks of therapy. Progression is defined as a radiologic change that is deemed by the treating oncologist to need a change in therapy. Pseudo-progression would be accounted for as it typically occurs within the first 2 months of treatment and on subsequent imaging that would occur within the first 18 weeks would be validated as pseudo-progression. * Patients must NOT have received any class of drugs targeting TIM3 pathway Exclusion Criteria Cohort A: * Participants who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to the first dose of study medication. * Participants who are receiving any other investigational agents. * Patient has known active central nervous system metastases and/or carcinomatous meningitis. Patients with previously treated brain metastases may participate provided they are clinically stable, have no evidence of new or enlarging brain metastases on repeat imaging at least 4 weeks after treatment, and are off steroids 3 days prior to dosing with study treatment. Stable brain metastases by this definition should be established prior to the first dose of study treatment. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to dostarlimab or cobolimab. Known severe hypersensitivity reactions to monoclonal antibodies (Grade \>=3, NCI CTCAE 5.0). * Participants with a history of treatment anti-CTLA4, TIM3 antagonist, or other investigational agents that target immune checkpoint inhibitors * Participants who had prior anti-PD-1 or anti-PD-L1 therapy * History of interstitial lung disease * Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent. Patients with diabetes type I, psoriasis, hypo- or hyperthyroid disease not requiring immunosuppressive treatment are eligible. * Known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS), that does not meet the following criteria: a. subject with HIV infection is eligible if undetectable HIV RNA within 4 weeks of study drug administration, b. absence of acquired immunodeficiency syndrome defining opportunistic infections within the past 12 months prior to study enrollment, and c. is on antiretroviral therapy for at least 4 weeks prior to study enrollment. * Patient has known active hepatitis B (eg, hepatitis B surface antigen reactive) or hepatitis C (eg, positive hepatitis C antibody and hepatitis C virus ribonucleic acid qualitative is detected) or known active hepatic cirrhosis. For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * Subjects requiring hormone replacement with corticosteroids are eligible if the steroids are administered only for hormone replacement and at doses of \<=5 mg or 5 mg equivalent prednisone per day. * Uncontrolled current 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 or prior use of immunosuppressive medication within 7 days prior to enrollment with the following exceptions to this exclusion criterion: * Intranasal, inhaled, topical steroids or local steroid injections (e.g. intra-articular injection); * at physiologic doses not to exceed 5 mg/day prednisone or equivalent; * Steroids at premedication for hypersensitivity reactions (e.g., CT scan premedication) * Severe gastrointestinal conditions such as clinical or radiographic evidence of bowel obstruction within 4 weeks prior to study entry, uncontrolled diarrhea in the last 4 weeks prior to enrollment, or history of inflammatory bowel disease. * Live vaccination within 4 weeks of the first dose of dostarlimab and cobolimab and while on trial is prohibited except for administration of inactivated vaccines. * Participants may not use natural herbal products or other "folk remedies" while participating in this study. Herbal medications include, but are not limited to St. John's Wort, Kava, ephedra, ginkgo biloba, dehydroepiandrosterone (DHEA), yohimbe, saw palmetto, and ginseng. * Prior organ transplantation, including allogeneic stem-cell transplantation. * Pregnant women are excluded from this study because dostarlimab and cobolimab are immunomodulatory agents with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with dostarlimab and cobolimab, breastfeeding should be discontinued if the mother is treated with dostarlimab and cobolimab. * Individuals with a history of a different malignancy are ineligible except for the following circumstances: individuals who have been disease-free for at least 5 years prior to study enrollment or if they are deemed by the investigator to be low risk for recurrence of that malignancy. Individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: breast cancer in situ and basal cell or squamous cell carcinoma of skin Exclusion Criteria Cohort B: * Participants who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to the first dose of study medication. * Participants who are receiving any other investigational agents. * Patient has known active central nervous system metastases and/or carcinomatous meningitis. Patients with previously treated brain metastases may participate provided they are clinically stable, have no evidence of new or enlarging brain metastases on repeat imaging at least 4 weeks after treatment, and are off steroids 3 days prior to dosing with study treatment. Stable brain metastases by this definition should be established prior to the first dose of study treatment. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to dostarlimab or cobolimab. Known severe hypersensitivity reactions to monoclonal antibodies (Grade \>=3, NCI CTCAE 5.0). * Participants with a history of treatment anti-CTLA4, TIM3 antagonist, or other investigational agents that target immune checkpoint inhibitors * Participants who had prior anti-PD-1 or anti-PD-L1 therapy, except those that meet criteria for 3.3.3, patients may have received prior pembrolizumab either as first-line therapy in combination with platinum-based chemotherapy with or without bevacizumab and did not progress in the first 18 weeks of therapy OR patients who received pembrolizumab as a subsequent line of therapy and who did not progress in the first 18 weeks of therapy. Progression is defined as a radiologic change that is deemed by the treating oncologist to need a change in therapy. * Participants who had received prior pembrolizumab and developed immune-related adverse events requiring systemic steroids, dose hold, or discontinuation * History of interstitial lung disease * Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent. Patients with diabetes type I, psoriasis, hypo- or hyperthyroid disease not requiring immunosuppressive treatment are eligible. * Known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS), that does not meet the following criteria: a. subject with HIV infection is eligible if undetectable HIV RNA within 4 weeks of study drug administration, b. no acquired immunodeficiency syndrome defining opportunistic infections within the past 12 months prior to study enrollment and c. is on antiretroviral therapy for at least 4 weeks prior to study enrollment. * Patient has known active hepatitis B (eg, hepatitis B surface antigen reactive) or hepatitis C (eg, positive hepatitis C antibody and hepatitis C virus ribonucleic acid qualitative is detected) or known active hepatic cirrhosis. For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * Subjects requiring hormone replacement with corticosteroids are eligible if the steroids are administered only for hormone replacement and at doses of \<=5 mg or 5 mg equivalent prednisone per day. * 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 or prior use of immunosuppressive medication within 7 days prior to enrollment with the following exceptions to this exclusion criterion: * Intranasal, inhaled, topical steroids or local steroid injections (e.g. intra-articular injection); * at physiologic doses not to exceed 5 mg/day prednisone or equivalent; * Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication) * Severe gastrointestinal conditions such as clinical or radiographic evidence of bowel obstruction within 4 weeks prior to study entry, uncontrolled diarrhea in the last 4 weeks prior to enrollment, or history of inflammatory bowel disease. * Live vaccination within 4 weeks of the first dose of dostarlimab and cobolimab and while on trial is prohibited except for administration of inactivated vaccines. * Participants may not use natural herbal products or other "folk remedies" while participating in this study. Herbal medications include, but are not limited to St. John's Wort, Kava, ephedra, ginkgo biloba, dehydroepiandrosterone (DHEA), yohimbe, saw palmetto, and ginseng. * Prior organ transplantation, including allogeneic stem-cell transplantation. * Pregnant women are excluded from this study because dostarlimab and cobolimab are immunomodulatory agents with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with dostarlimab and cobolimab, breastfeeding should be discontinued if the mother is treated with dostarlimab and cobolimab. * Individuals with a history of a different malignancy are ineligible except for the following circumstances: individuals who have been disease-free for at least 5 years prior to study enrollment or if they are deemed by the investigator to be low risk for recurrence of that malignancy. Individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: breast cancer in situ and basal cell or squamous cell carcinoma of skin