RESOLVE: Abemaciclib + Letrozole +/- Metformin or Gedatolisib in Endometrial Cancer

Inclusion Criteria:

* Participants must have cytologically or histologically confirmed endometrial cancer that is recurrent or metastatic and/or resistant to standard therapies, or for which no standard therapy is available. Participants enrolled in the second stage of Cohort 1A, or into Cohort 3, 6 and 7, must have histologically confirmed either i) endometrioid endometrial cancer or ii) endometrial carcinosarcoma with endometrioid epithelial component
* Participants must have ER-positive disease, defined as ≥ 1 percent of tumor cell nuclei being immunoreactive by immunohistochemistry (IHC). If multiple analyses have been performed, judgment should be based on the most recent biopsy or pathology specimen analyzed in a CLIA-certified laboratory.
* Participants must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥20 mm with conventional techniques or as ≥10 mm with spiral CT scan, MRI, or calipers by clinical exam.
* Age ≥ 18 years
* ECOG performance status of 0 or 1
* Participants must have normal organ and bone marrow function as defined below:

  * Absolute neutrophil count ≥ 1,500/mcL
  * Platelets ≥ 100,000/mcL
  * Total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN). Patients with Gilbert's syndrome with a total bilirubin \</= 2.0 times ULN and direct bilirubin within normal limits are permitted.
  * AST(SGOT)/ALT(SGPT) ≤ 3× institutional ULN
  * Creatinine ≤ 1.5 × institutional ULN, OR
  * Creatinine clearance ≥ 60 mL/min/1.73 m2 for participants with creatinine levels above institutional normal.
* For cohorts 6 and 7, patients must not have remaining ovarian function to be included. Women who have ovarian function are eligible but must be placed on hormonal suppression.
* The effects of the study agents on the developing human fetus are unknown. For this reason, women of child-bearing potential must agree to use a medically approved contraceptive method during the treatment period and for 3 months following the last dose of study agent. Contraceptive methods may include an intrauterine device (IUD) or barrier method. If condoms are used as a barrier method, a spermicidal agent should be added as a double barrier protection. Should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately. A negative serum pregnancy test is required for study entry from women of childbearing potential.
* Ability to understand and the willingness to sign a written informed consent document.
* Ability to swallow and retain oral medication.
* Participants can have received an unlimited number of prior therapies.
* Participants must have archival tissue available for analysis in the form of a formalin-fixed paraffin embedded (FFPE) block or unstained slides. Note: confirmation of availability of archival tissue is the only requirement for eligibility, archival tissue does not need to be received by the study team prior to enrollment
* For Cohorts 6 and 7, participants must have HbA1c ≤6.4% and fasting plasma glucose (FPG) ≤140 mg/dL.
* For Cohort 6 and 7, patients must have wildtype TP53 as assessed either by immunohistochemistry or any CLIA-certified next-generation sequencing assay.
* For Cohort 7, patients must have received prior CDK4/6 inhibitor therapy and developed disease progression as deemed by the investigator. Patients who have stopped CDK4/6 inhibitor therapy because of intolerance are ineligible.

Exclusion Criteria:

* Participants who have had chemotherapy, immune therapy, other investigational therapy, or major surgery within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to the first dose of study medication. Previous hormonal therapy, including prior letrozole, is allowed and there is no required washout period for hormonal therapy.
* Participants who have had tyrosine kinase inhibitor (TKI) therapy within 5 half-lives of study entry.
* Participants who have had radiation therapy within 2 weeks of the first dose of study medication.
* Participants who have received previous treatment with CDK4/6 inhibitors, including but not limited to previous abemaciclib therapy. For Cohort 7, patients must have received prior treatment with CDK4/6 inhibitors.
* Participants who are currently receiving metformin therapy (if enrolling to Cohort 3).
* Participants who have impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of the study drugs
* Participants with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events.
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to the study agents that the participant will be administered.
* Participants who at the time of study enrollment are known to require concomitant therapy with moderate or strong CYP3A4 inducers, or strong inhibitors of CYP3A4. Due to potential drug interactions, concomitant use of these medications is not permitted for the duration of treatment on trial. Participants are eligible for study entry if an appropriate substitution is made prior to the first dose of study medication.
* 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.
* Use of known QT-prolonging drugs during screening or expected requirement for use during study therapy.
* Participants with histories or evidence of cardiovascular risk including any of the following: acute coronary syndromes (i.e. myocardial infarction or angina), coronary angioplasty, or stenting within 6 months prior to study enrollment.
* Pregnant women are excluded from this study because the study agents are anti-cancer 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 the study agents, breastfeeding must be discontinued if the mother is treated on trial.
* Individuals with a history of a different malignancy are ineligible with the following exceptions: individuals who have been treated and are disease-free for a minimum of 5 years prior to study enrollment, or individuals who are deemed by the treating investigator to be at low risk for disease recurrence. Additionally, individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: basal or squamous cell carcinomas of the skin, and breast or cervical carcinomas in situ.
* Known HIV-positive participants are ineligible because of the increased risk of lethal infections when treated with marrow-suppressive therapy.
* Participants with a history of uncontrolled hypertension despite optimal medical management, defined as systolic blood pressure \> 150 mmHg or diastolic blood pressure \> 90 mmHg.
* For Cohorts 6 and 7: Inability to determine the corrected QT interval using Fridericia's formula (QTcF) on the ECG (i.e., unreadable or not interpretable) or QTcF\>480 msec (determined by mean of triplicate ECGs at screening).
* For Cohorts 6 and 7, participants with type 1 diabetes or uncontrolled type 2 diabetes.
* For Cohorts 6 and 7, participants who have previously received any PI3K pathway inhibitors are ineligible. Up to 10 patients in Cohort 6 and up to 10 patients in Cohort 7 may have received prior mTOR inhibitor therapy such as everolimus.