A Study of Sapanisertib, Combination of Sapanisertib With MLN1117, Paclitaxel and Combination of Sapanisertib With Paclitaxel in Women With Endometrial Cancer

Inclusion Criteria: 1. Histologic or cytologic diagnosis of endometrial carcinoma (including endometrioid, serous, mixed adenocarcinoma, clear-cell carcinoma, or carcinosarcoma). 2. Evidence that the endometrial cancer is advanced, recurrent, or persistent and has relapsed or is refractory to curative therapy or established treatments. 3. At least 1 prior platinum-based chemotherapeutic regimen, but not more than 2 prior chemotherapeutic regimens, for management of endometrial carcinoma. Prior treatment may include chemotherapy, chemotherapy/radiation therapy, and/or consolidation/maintenance therapy. Chemotherapy administered in conjunction with primary radiation as a radio-sensitized therapy will be considered a systemic chemotherapy regimen. 4. Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1, defined as at least 1 lesion that can be accurately measured in at least 1 dimension (longest diameter to be recorded). Each lesion must be greater than or equal to (\>=) 10 millimeter (mm) in long axis when measured by computed tomography (CT), magnetic resonance imaging (MRI), or caliper measurement by clinical exam. Lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI. 5. Tumor accessible and participant consents to undergo fresh tumor biopsies. 6. Female participants 18 years or older. 7. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 8. Female participants who: * Are postmenopausal for at least 1 year before the screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential, agree to practice 1 highly effective method of contraception and 1 additional effective (barrier) method at the same time, from the time of signing the informed consent through 90 days (or longer, as mandated by local labeling \[example, United States Prescribing Information (USPI), Summary of Product Characteristics (SmPC), etc.\]) after the last dose of study drug, OR * Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the participant. (Periodic abstinence \[example, calendar, ovulation, symptothermal, postovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together.) 9. Clinical laboratory values as specified below within 4 weeks before the first dose of study drug: * Bone marrow reserve consistent with absolute neutrophil count (ANC) \>= 1500 per micro liter (/mcL); platelet count \>= 100,000/mcL; hemoglobin A1c (HbA1c) less than (\<) 6.5 percent (%). * Total bilirubin must be less than or equal to (\<=) 1.5 \* the upper limit of normal (ULN). * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) must be \<= 2.5 \* the upper limit of the normal range. AST and ALT may be elevated up to 5 times the ULN if their elevation can be reasonably ascribed to the presence of metastatic disease in liver. * Creatinine clearance \>= 50 milliliter per minute per 1.73 square meter (mL/min/1.73 m\^2) based either on Cockcroft-Gault estimate or based on a 12- or 24-hour urine collection. * Fasting serum glucose \< 130 milligram per deciliter (mg/dL) and fasting triglycerides \<= 300 mg/dL. 10. Ability to swallow oral medications, willingness to perform mucositis prophylaxis, and suitable venous access for the study-required blood sampling. 11. Voluntary written consent must be given before performance of any study-related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the participant at any time without prejudice to future medical care. Exclusion Criteria: 1. Positive serum pregnancy test during the screening period or a positive urine pregnancy test on Day 1 before first dose of study drug. Women who are lactating and breastfeeding are not eligible. 2. Previous treatment with any weekly taxane regimen. 3. History of severe hypersensitivity reactions to paclitaxel or any of its excipients. 4. Previous treatment with phosphoinositide 3-kinase (PI3K), serine/threonine-specific protein kinase (AKT), dual PI3K/ mammalian (or mechanistic) target of rapamycin (mTOR) inhibitors, target of rapamycin complex 1/2 (TORC1/2) inhibitors or TORC1 inhibitors. 5. Initiation of treatment with hematopoietic growth factors, transfusions of blood and blood products, or systemic corticosteroids (either intravenous \[IV\] or oral steroids, excluding inhalers) within 1 week before administration of the first dose of study drug (participants already receiving erythropoietin on a chronic basis for \>=4 weeks are eligible). 6. Participants who are taking proton pump inhibitors (PPIs) within 7 days of the first dose of study drug or who require treatment with PPIs throughout the trial or those who are taking H2 receptor antagonists within 24 hours of the first dose of study drug. 7. A prothrombin time (PT) or activated partial thromboplastin time (aPTT) above the ULN or a history of a coagulopathy or bleeding disorder. 8. Known hepatitis B surface antigen-positive, or known or suspected active hepatitis C infection. 9. Sensory or motor neuropathy \>= Grade 2. 10. Central nervous system (CNS) metastasis, endometrial leiomyosarcoma, or endometrial stromal sarcoma. 11. Manifestations of malabsorption due to prior gastrointestinal surgery, gastrointestinal disease, or for some other reason that may alter the absorption of sapanisertib or MLN1117. In addition, participants with enteric stomata are also excluded. 12. Other clinically significant co-morbidities, such as uncontrolled pulmonary disease, active CNS disease, active infection, or any other condition that could compromise participation of the participant in the study. 13. Known human immunodeficiency virus infection. 14. History of any of the following within the last 6 months before administration of the first dose of study drug: * Ischemic myocardial event, including angina requiring therapy and artery revascularization procedures. * Ischemic cerebrovascular event, including transient ischemic attack and artery revascularization procedures. * Requirement for inotropic support (excluding digoxin) or serious (uncontrolled) cardiac arrhythmia (including atrial flutter/fibrillation, ventricular fibrillation, or ventricular tachycardia). * Placement of a pacemaker for control of rhythm. * New York Heart Association Class III or IV heart failure. * Pulmonary embolism. 15. Significant active cardiovascular or pulmonary disease before administration of the first dose of study drug, including: * Uncontrolled hypertension (that is, either systolic blood pressure \> 180 millimeter of mercury \[mm Hg\] or diastolic blood pressure \> 95 mm Hg). * Pulmonary hypertension. * Uncontrolled asthma or oxygen saturation \< 90% by arterial blood gas analysis or pulse oximetry on room air. * Significant valvular disease; severe regurgitation or stenosis by imaging independent of symptom control with medical intervention; or history of valve replacement. * Medically significant (symptomatic) bradycardia. * History of arrhythmia requiring an implantable cardiac defibrillator. * Baseline prolongation of the rate-corrected QT interval (QTc; example, repeated demonstration of QTc interval \> 480 millisecond \[ms\], or history of congenital long QT syndrome, or torsades de pointes). 16. Diagnosed or treated for another malignancy within 2 years before administration of the first dose of study drug or previously diagnosed with another malignancy and have any evidence of residual disease. Participants with non-melanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection. 17. Participants with endometrioid histology and histologically confirmed expression of estrogen receptors (ER) and/or progesterone receptors (PgR) who have not received prior endocrine therapy and for whom endocrine therapy is currently indicated.