This phase III trial studies how well the combination of pembrolizumab, paclitaxel and carboplatin works compared with paclitaxel and carboplatin alone in treating patients with endometrial cancer that is stage III or IV, or has come back after a period of improvement (recurrent). Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Paclitaxel and carboplatin are chemotherapy drugs used as part of the usual treatment approach for this type of cancer. This study aims to assess if adding immunotherapy to these drugs is better or worse than the usual approach for treatment of this cancer.

PRIMARY OBJECTIVE: I. To evaluate the efficacy of pembrolizumab (MK-3475) in combination with paclitaxel and carboplatin in patients with advanced stage (measurable stage III or IVA), stage IVB and recurrent endometrial cancer. SECONDARY OBJECTIVES: I. To determine the nature, frequency and degree of toxicity as assessed by Common Terminology Criteria for Adverse Events (CTCAE) for each treatment arm. II. To evaluate blinded independent central review (BICR) assessed or investigator assessed objective response rate (ORR) as assessed by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 by treatment arm and by mismatch repair (MMR) immunohistochemistry (IHC) status in patients who enter the study with measurable disease. III. To evaluate BICR assessed or investigator assessed duration of response (DOR) by treatment arm and by MMR IHC status in patients who enter the study with measurable disease. IV. To evaluate the effect of pembrolizumab (MK-3475) on overall survival (OS) in patients with mismatch repair protein proficient (pMMR) or mismatch repair deficiency (dMMR). V. To determine whether the addition of pembrolizumab (MK-3475) to standard combination chemotherapy is associated with improved patient reported physical function as measured with the Patient-Reported Outcomes Measurement Information System (PROMIS)-physical function scale (short form), quality of life as measured with the Functional Assessment of Cancer Therapy (FACT) - Endometrial Trial Outcome Index (En TOI) and worsened fatigue as measured with the PROMIS-Fatigue scale (short form) in the pMMR patients. VI. To determine concordance between institutional MMR IHC testing and centralized MMR IHC. EXPLORATORY OBJECTIVES: I. To explore the correlation between patient-reported physical function as measured with the PROMIS-physical function scale (short form) and quality of life as measure with the FACT-En TOI. II. To explore whether the addition of pembrolizumab (MK-3475) to standard combination chemotherapy is associated with self-reported neurotoxicity as measured with the FACT/Gynecologic Oncology Group Neurotoxicity (GOG-Ntx) subscale (short) and the extent to which patients differ on their self-reported bother from side effects of cancer therapy in the pMMR patients. III. To evaluate the efficacy of pembrolizumab (MK-3475) in combination with paclitaxel and carboplatin in patients with advanced stage (measurable stage III or IVA), stage IVB and recurrent endometrial cancer by Programmed Death Ligand 1 (PD-L1) IHC (positive versus \[vs\] negative). IV. To assess the association between PD-L1 IHC (positive vs negative) and mismatch repair status (pMMR and dMMR). OUTLINE: Patients are randomized to 1 of 2 arms. ARM I: COMBINATION PHASE: Patients receive placebo intravenously (IV) over 30 minutes on day 1 of each cycle, paclitaxel IV over 3 hours on day 1 of each cycle, and carboplatin IV over 30-60 minutes on day 1 of each cycle. Treatment repeats every 3 weeks for 6 cycles in the absence of disease progression or unacceptable toxicity. Patients with stable disease (SD) or partial response (PR) who still have measurable disease may continue treatment for up to a total 10 cycles (if deemed necessary by the treating physician) in the absence of disease progression or unacceptable toxicity. MAINTENANCE PHASE: Patients receive placebo IV over 30 minutes on day 1 of each cycle. Treatment repeats every 6 weeks for up to 14 cycles in the absence of disease progression or unacceptable toxicity. On February 6, 2023, all patient treatment assignments were unblinded. Patients randomized to Arm I will not receive additional placebo infusions. ARM II: COMBINATION PHASE: Patients receive pembrolizumab IV over 30 minutes on day 1 of each cycle, paclitaxel IV over 3 hours on day 1 of each cycle, and carboplatin IV over 30-60 minutes on day 1 of each cycle. Treatment repeats every 3 weeks for 6 cycles in the absence of disease progression or unacceptable toxicity. Patients with SD or PR who still have measurable disease may continue treatment for up to a total of 10 cycles (if deemed necessary by the treating physician) in the absence of disease progression or unacceptable toxicity. MAINTENANCE PHASE: Patients receive pembrolizumab IV over 30 minutes on day 1 of each cycle. Treatment repeats every 6 weeks for up to 14 cycles in the absence of disease progression or unacceptable toxicity. Patients undergo computed tomography (CT) scan throughout the study. After completion of study treatment, patients are followed up every 3 months for 2 years and then every 6 months for 3 years.