Sapanisertib and Metformin in Treating Patients With Advanced or Metastatic Relapsed or Refractory Cancers

Inclusion: 1. Male or female patients 18 years or older. 2. 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of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care. 3. Female patients 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 one 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 \[eg USPI, SmPC, etc\] 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 patient (Periodic abstinence \[e.g, calendar, ovulation, symptothermal, postovulation methods\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together.) MUST have a negative serum or urine pregnancy test within 7 days of initiating protocol treatment unless prior hysterectomy or menopause (defined as 12 consecutive months without menstrual activity). 4. CONTINUED FROM #3: Patients should not become pregnant or breastfeed while on this study. The effects of TAK-228 and metformin on the developing human fetus are unknown. Should a woman become pregnant or suspect she is pregnant, she should inform her treatment physician immediately. Male patients, even if surgically sterilized (ie, status post-vasectomy), who: Agree to practice highly effective barrier contraception during the entire study treatment period and through 120 days 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 patient, as described in #3 above. Agree not to donate sperm during the course of this study or within 120 days after receiving their last dose of study drug. 5. Patients must have a diagnosis of advanced or metastatic malignancy that is refractory to standard therapies, who have relapsed after standard therapy, or whose cancers have no standard therapy that induces a CR rate of at least 10% or improves survival by at least three months. 6. Eastern Cooperative Oncology Group (ECOG) performance status and/or other performance status \</= 1. 7. Adequate organ function, as specified below, within 7 days before the first dose of study drug: a) Bone marrow reserve consistent with: absolute neutrophil count (ANC) \>/= 1.5 x 10\^9/L; platelet count \>/= 100 x 10\^9/L; hemoglobin \>/= 9 g/dL without transfusion within 1 week preceding study drug administration; b) Hepatic: total bilirubin \</= 1.5 x upper limit of normal (ULN), transaminases (aspartate aminotransferase/serum glutamic oxaloacetic transaminase-AST/SGOT and alanine aminotransferase/serum glutamic pyruvic transaminase-ALT/SGPT) \</= 2.5 x ULN (\</= 5 x ULN if liver metastases are present); c) Renal: creatinine clearance \>/=50 mL/min based either on Cockroft-Gault estimate or based on urine collection (12 or 24 hour); d) Metabolic: fasting serum glucose (\</= 130 mg/dL) and fasting triglycerides \</= 300 mg/dL. 8. Ability to swallow oral medications. 9. Patients with diabetes are allowed and may be on antidiabetic treatment other than Metformin. The diabetes must be under control within normal range (HbA1C \</=7%). 10. Patients must be at least 5 half-lives beyond previous treatment with metformin and currently not taking metformin. 11. Patients must be \>/= 4 weeks beyond previous treatment of any chemotherapy, other investigational therapy, hormonal, biological, targeted agents or radiotherapy, and must have recovered to \</= grade 1 or previous baseline for each toxicity. Exception: Patients may have received palliative low dose radiotherapy to the limbs 1-4 weeks before this therapy provided pelvis, sternum, scapulae, vertebrae, or skull were not included in the radiotherapy field. Patients who have received non-chemotherapeutic biological agents will need to wait at least 5 half-lives or 4 weeks, whichever is shorter, from the last day of treatment of non-chemotherapeutic biological agents. 12. Patients must have evaluable or measurable disease by RECIST 1.1 criteria. These measurements will be done by the Quantitative Imaging Analysis Core (QIAC) group. Exclusion: 1. Female patients who are both lactating and breastfeeding or have a positive serum pregnancy test during the screening period or a positive urine pregnancy test on Day 1 before first dose of study drug. 2. Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol. 3. Participation in other clinical trials, including those with other investigational agents not included in this trial, within 5 half lives of those investigational agents before the start of this trial and throughout the duration of this trial. 4. Manifestations of malabsorption due to prior gastrointestinal (GI) surgery, GI disease, or for an unknown reason that may alter the absorption of TAK-228. In addition, patients with enteric stomata are also excluded. 5. Poorly controlled diabetes mellitus defined as glycosylated hemoglobin (HbA1c) \> 7%; patients with a history of transient glucose intolerance due to corticosteroid administration may be enrolled in this study if all other inclusion/exclusion criteria are met. 6. History of any of the following within the last 6 months prior to study entry: Ischemic myocardial event, including angina requiring therapy and artery revascularization procedures; Ischemic cerebrovascular event, including TIA 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 (NYHA) Class III or IV heart failure; Pulmonary embolism. 7. Significant active cardiovascular or pulmonary disease at the time of study entry, including: Uncontrolled high blood pressure (i.e., systolic blood pressure \>150mm Hg, diastolic blood pressure \> 90 mm Hg). Use of anti-hypertensive agents to control hypertension before Cycle1 Day 1 is allowed.; Pulmonary hypertension; Uncontrolled asthma or O2 saturation \< 90% by ABG (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) (e.g., repeated demonstration of QTc interval \> 480 milliseconds, or history of congenital long QT syndrome, or torsades de pointes). 8. Previous treatment with dual PI3K/mTOR inhibitors, TORC1/2 inhibitors or TORC1 inhibitors 9. Patients receiving corticosteroids (either IV or oral steroids, excluding inhalers or low-dose hormone replacement therapy) within 1 week before administration of the first dose of study drug. 10. Other clinically significant co-morbidities, such as uncontrolled pulmonary disease, active central nervous system disease, active infection, or any other condition that could compromise participation of the patient in the study. 11. Patients with major surgery within 30 days prior to entering the study. 12. History of hypersensitivity to TAK-228 or metformin. 13. Patients who have a history of brain metastasis are eligible for the study provided that all the following criteria are met: A. Brain metastases which have been treated B. No evidence of disease progression for \>/= 3 months before the first dose of study drug. C. No hemorrhage after treatment D. Off-treatment with dexamethasone for 4 weeks before administration of the first dose of TAK-228 E. No ongoing requirement for dexamethasone or anti-epileptic drugs 14. Known human immunodeficiency virus infection. 15. Known hepatitis B surface antigen-positive, or known or suspected active hepatitis C infection. 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. Patients with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection. 17. Daily or chronic use of a proton pump inhibitor (PPI) and/or having taken a PPI within 7 days before receiving the first dose of study drug.