Paclitaxel and TAK-228 in Urothelial Carcinoma

Inclusion Criteria: 1. Male or female patients 18 years or older. 2. Patients must have a diagnosis of metastatic or advanced histologically confirmed UC (urothelial cancer). Mixed histologies are allowed. 3. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1. 4. 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 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 \[e.g., USPI, SmPC, etc,\]) 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). Male patients, even if surgically sterilized (i.e., 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. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods for the female partner\], withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception. Female and male condoms should not be used together). * Agree not to donate sperm during the course of this study or within 120 days after receiving their last dose of study drug 5. Screening clinical laboratory values as specified below: * Bone marrow reserve consistent with: absolute neutrophil count (ANC) ≥ 1.5 x 109/L; platelet count ≥ 100 x 109/L; hemoglobin ≥ 9 g/dL without transfusion within 1 week preceding study drug administration. * 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); * Renal: creatinine clearance ≥50 mL/min based either on Cockroft-Gault estimate or based on urine collection (12 or 24 hour); * Metabolic: Glycosylated hemoglobin (HbA1c) \<7.0%, fasting serum glucose (≤ 130 mg/dL) and fasting triglycerides ≤ 300 mg/dL. 6. Ability to swallow oral medications. 7. 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. 8. Patients who have a history of brain metastasis are eligible for the study provided that all the following criteria are met: * Brain metastases which have been treated. * No evidence of disease progression for ≥3 months before the first dose of study drug. * No hemorrhage after treatment. * Off-treatment with dexamethasone for 4 weeks before administration of the first dose of TAK-228. * No ongoing requirement for dexamethasone or anti-epileptic drugs. 9. Patients having received prior systemic chemotherapy treatment for UC, with no limit for number of prior systemic chemotherapeutic or investigational treatment regimens. Specifically, subjects must meet one or more of the following criteria: • Progression after treatment with a regimen that includes a platinum salt (e.g. - carboplatin or cisplatin) for Stage IV disease. OR • Disease recurrence within one years from the date of last dose of chemotherapy or surgery until day the informed consent is signed) after neoadjuvant or adjuvant treatment with a regimen that includes a platinum salt. 10. Measurable disease, as defined by RECIST v.1.1. If all sites of measurable disease have been irradiated, one site must have demonstrated growth after irradiation. 11. Normal (or within 5% of lower limit) left ventricular ejection fraction Exclusion Criteria: 1. Prior treatment with paclitaxel for UC (in any setting - neoadjuvant, adjuvant or for metastatic disease). Patients treated with prior docetaxel are eligible. 2. Previous treatment with PI3K, AKT, dual PI3K/mTOR inhibitors, TORC1/2 inhibitors or TORC1 inhibitors. 3. 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. 4. Poorly controlled diabetes mellitus defined as HbA1c \> 7%; subjects with a history of transient glucose intolerance due to corticosteroid administration are allowed in this study if all other inclusion/exclusion criteria are met. 5. Presence of central nervous system metastasis, except for those matching requirements detailed per inclusion criterion 8. 6. Evidence of severe or uncontrolled systemic disease or any concurrent condition which in the Investigator's opinion makes it undesirable for the subject to participate in the trial or which would jeopardize compliance with the protocol. 7. 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 (See Appendix C) * Pulmonary embolism. 8. Significant active cardiovascular or pulmonary disease at the time of study entry, including: * Uncontrolled high blood pressure (i.e., systolic blood pressure \>180 mm Hg, diastolic blood pressure \> 95 mm Hg). Use of anti-hypertensive agents to control hypertension before Cycle 1 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). 9. History of arrhythmia (multifocal premature ventricular contractions (PVCs), bigeminy, trigeminy, ventricular tachycardia, or uncontrolled atrial fibrillation), which is symptomatic or requires treatment (CTCAE grade 3) or asymptomatic sustained ventricular tachycardia. 10. Controlled atrial fibrillation such as with medication or cardioversion is not excluded. 11. Treatment with systemic corticosteroids (either IV or oral steroids, excluding inhalers or low-dose hormone replacement therapy, i.e., prednisone ≤10mg or its equivalent) within 1 week before administration of the first dose of study drug. 12. Women who are currently pregnant or breast feeding. 13. Receipt of any investigational agent, chemotherapy or radiation therapy within 21 days prior to Study Day 1. 14. Any unresolved non-hematologic toxicity greater than CTCAE grade 1 from previous anti-cancer therapy (other than alopecia). 15. Major surgery within 4 weeks, or incompletely healed surgical incision before starting study therapy 16. Grade 2 or greater peripheral neuropathy 17. 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 non-melanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection. 18. Other clinically significant co-morbidities, such as uncontrolled pulmonary disease, active central nervous system disease, active infection, or any other condition that could compromise the patient's participation in the study. 19. Known human immunodeficiency virus infection 20. Known hepatitis B surface antigen-positive, or known or suspected active hepatitis C infection. 21. Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol 22. Patients 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.