A Phase II/III Study of Paclitaxel/Carboplatin Alone or Combined with either Trastuzumab and Hyaluronidase-Oysk (HERCEPTIN HYLECTA) or Pertuzumab Trastuzumab and Hyaluronidase-ZZFX (PHESGO) in HER2 Positive, Stage I-IV Endometrial Serous Carcinoma or Carcinosarcoma.

Inclusion Criteria: - Federation of Gynecology and Obstetrics (FIGO) 2009 stage IA-IVB, non-recurrent, chemotherapy (chemo)-naive, HER2-positive endometrial cancer. The following endometrial cancer types are eligible: - Serous - Other endometrial cancers (including clear cell, endometrioid, mixed epithelial, dedifferentiated/undifferentiated) - Carcinosarcoma - NOTE: Endometrial cancers that are mismatch repair deficient (dMMR) by IHC are not eligible - Histologic confirmation of the original primary tumor is required. Submission of surgical pathology report (or endometrial biopsy pathology report in patients who never undergo hysterectomy) is required - Patients must be within 8 weeks of primary surgery (or endometrial biopsy in patients who never undergo hysterectomy) at the time of study registration - Patients may have measurable disease, non-measurable disease, or no measurable disease. In patients with measurable disease, lesions will be defined and monitored by RECIST v 1.1. Measurable disease is 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 or magnetic resonance imaging (MRI). Lymph nodes must be >= 15 mm in short axis when measured by CT or MRI - For patients with uterine-confined (stage I) disease, the tumor must be invasive into the myometrium. Any amount of myoinvasion is acceptable for eligibility. Patients with non-invasive disease, endometrial intraepithelial carcinoma alone, or disease confined to a polyp will be excluded - All patients must have tumors that are HER2 positive as defined by American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) 2018 Breast Cancer guidelines (https://documents.cap.org/documents/algorithim-evaluation-her2.pdf.) IHC and ISH testing will be done locally, at each participating institution and interpreted by local pathologists. In general HER2 positivity is defined as any of the following: - 3+ immunohistochemistry (IHC), - 2+ IHC with positive in situ hybridization (ISH) Alternatively, patients could be eligible if next generation sequencing (NGS) demonstrates HER2 (ERBB2) amplification. NGS testing can be performed through any designated labs as per the National Cancer Institute (NCI) MATCH/NCI Combo-MATCH trial (https://ecog-acrin.org/nci-match-eay131-designated-labs). Pathology report showing results of institutional HER2 testing (or NGS testing results) must be submitted. Sites must submit all results available (IHC, ISH, and NGS) - Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 - Age >= 18 - Platelets >= 100,000/mcl (within 14 days prior to registration) - Absolute neutrophil count (ANC) >= 1,500/mcl (within 14 days prior to registration) - Creatinine =< 1.5 x institutional/laboratory upper limit of normal (ULN) or estimated Glomerular filtration rate (eGFR) >= 50 mL/min using either the Cockcroft-Gault equation, the Modification of Diet in Renal Disease Study, or as reported in the comprehensive metabolic panel/basic metabolic panel (eGFR) (within 14 days prior to registration) - Total serum bilirubin level =< 1.5 x ULN (patients with known Gilbert's disease who have bilirubin level =< 3 x ULN may be enrolled) (within 14 days prior to registration) - Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 3 x ULN (within 14 days prior to registration) - Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of registration are eligible for this trial - Although the uterus will have been removed in the vast majority of patients, for patients of child-bearing potential: negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test is required. Patients will be considered of non-reproductive potential if they are either: - Postmenopausal (defined as at least 12 months with no menses without an alternative medical cause; in women < 45 years of age, a high follicle stimulating hormone [FSH] level in the postmenopausal range may be used to confirm a postmenopausal state in women not using hormonal contraception or hormonal replacement therapy. In the absence of 12 months of amenorrhea, a single FSH measurement is insufficient); OR - Have had a hysterectomy and/or bilateral oophorectomy, bilateral salpingectomy or bilateral tubal ligation/occlusion at least 6 weeks prior to registration - Have a congenital or acquired condition that prevents childbearing - Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial - Patients with evidence of chronic hepatitis B virus (HBV) infection must have an undetectable HBV viral load on suppressive therapy, if indicated - Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load - Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression - The patient or a legally authorized representative must provide study-specific informed consent prior to study entry and, for patients treated in the United States (U.S.), authorization permitting release of personal health information Exclusion Criteria: - Prior Therapy: - Patients must NOT have received prior chemotherapy, biologic therapy, or targeted therapy for treatment of endometrial carcinoma - Patients must NOT have received prior radiation therapy for treatment of endometrial carcinoma. Prior radiation includes external beam pelvic radiation therapy, external beam extended field pelvic/para-aortic radiation therapy, and/or intravaginal brachytherapy - NOTE: Vaginal brachytherapy for treatment of endometrial cancer is permitted during study treatment. Planned use of vaginal brachytherapy must be declared at time of registration - Patients may have received prior hormonal therapy for treatment of endometrial carcinoma. All hormonal therapy must be discontinued at least one week prior to registration - Patients may not have a planned interval cytoreduction or hysterectomy, prior to documentation of progression, after study registration - Patients may not have planned external beam radiotherapy, prior to documentation of progression, after study registration - Significant cardiovascular disease including: - Uncontrolled hypertension, defined as systolic > 150 mm Hg or diastolic > 90 mm Hg despite antihypertensive medications - Myocardial infarction or unstable angina within 6 months prior to registration - New York Heart Association functional classification II, III or IV - Serious cardiac arrhythmia requiring medication. This does not include asymptomatic, atrial fibrillation with controlled ventricular rate - Significant lung disease: dyspnea at rest grade 2 or greater (resulting from extensive tumor involvement or other causes), pneumonitis grade 2 or greater, interstitial lung disease grade 2 or greater, idiopathic pulmonary fibrosis, cystic fibrosis, Aspergillosis, active tuberculosis, or history of opportunistic infections (pneumocystis pneumonia or cytomegalovirus pneumonia) - Patients with uncontrolled intercurrent illness including, but not limited to: ongoing or active infection (except for uncomplicated urinary tract infection), uncontrolled interstitial lung disease, symptomatic congestive heart failure, or psychiatric illness/social situations that would limit compliance with study requirements - Treatment with strong CYP2C8 or CYP3A4 inhibitors or inducers within 14 days or 5 drug-elimination half-lives, whichever is longer, prior to registration - Women who are unwilling to discontinue nursing