Sapanisertib in Treating Patients With Locally Advanced or Metastatic Bladder Cancer With TSC1 and/or TSC2 Mutations

Inclusion Criteria: * Patients must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 * Must have a histologically confirmed transitional cell carcinoma (TCC, also known as urothelial carcinoma), locally advanced or metastatic * Patient must have TCCs tumors harboring a TSC1 or TSC2 mutation identified by a Clinical Laboratory Improvement Amendments (CLIA) certified laboratory * Unless the pre-screening was performed at Yale Clinical Molecular Pathology Lab (YCMPL), patients must have TCC tumor tissue available for submission in a form of at least 10 unstained slides or formalin-fixed paraffin-embedded (FFPE) block (FFPE block highly recommended and preferred) along with a buccal swab; if the number of slides is less than 10, a biopsy should be considered; if a biopsy is deemed unsafe, the case may be discussed with the study principal investigator (PI) and approval must be given for eligibility * Patient must have developed disease progression during or following treatment with at least one platinum-containing regimen (e.g., gemcitabine/cisplatin \[GC\], methotrexate-vinblastine-doxorubicin-cisplatin \[MVAC\], carboplatin, gemcitabine \[CarboGem\]) for inoperable locally advanced or metastatic urothelial carcinoma or disease recurrence, or must be unfit or ineligible for cisplatin-based chemotherapy; there is no restriction on the number of prior lines of chemotherapeutics agents received * Patients who progressed within 12 months of treatment with a platinum-containing neoadjuvant or adjuvant regimen are considered second-line patients; therefore, these patients may be also eligible * Patients who are unfit or ineligible for cisplatin-based chemotherapy as defined by any one of the following criteria are eligible for this trial: * Eastern Cooperative Oncology Group (ECOG) performance score of 2 * Creatinine clearance \< 60 mL/min * A hearing loss (measured by audiometry) of 25 dB at two contiguous frequencies * Grade \>= 2 peripheral neuropathy * ECOG performance status =\< 2 (Karnofsky \>= 60 %) * Life expectancy of greater than 12 weeks * Hemoglobin \>= 9 g/dL * Fasting serum glucose =\< 130 mg/dL * Glycosylated hemoglobin measurement (HbA1c) \< 7.0% * Fasting triglycerides =\< 300 mg/dL * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal (ULN) and =\< 5 ULN if liver metastases are present * Creatinine =\< 1.5 x upper normal institutional limits (UNL) OR creatinine clearance \>= 40 mL/min based either on Cockcroft-Gault estimate or based on urine collection (12 or 24 hour) * Patients with controlled diabetes are allowed on study; controlled diabetes is defined as fasting blood sugar (FBS) = 130 mg/dL or less, and patients whose FBS can be brought in this range with medical therapy are eligible for trial inclusion * The effects of MLN0128 (TAK-228) on the developing human fetus are unknown; fertility and developmental studies with MLN0128 (TAK-228) have not been conducted; on the basis of potential hazard of other mTOR inhibitors (i.e., rapamycin and other rapalogs) on the developing fetus, women of childbearing age should avoid becoming pregnant while taking any mTOR inhibitor including MLN0128 (TAK-228) * Female patients must: * Be postmenopausal for at least 1 year before the screening visit, OR * Be 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 \[e.g., United States product insert \[USPI\], 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 patient; NOTE: 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 postvasectomy), must: * 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 (NOTE: 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) * AND agree not to donate sperm during the course of this study or within 120 days after receiving their last dose of study drug * Ability to swallow oral medications * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy, immunotherapy, or investigational therapy, within 4 weeks (6 weeks for nitrosoureas or mitomycin C), or palliative radiotherapy within 2 weeks prior to the first dose of the study drug * Patients who have not recovered from adverse events due to prior anti-cancer therapy to grade 1 or baseline; patients with stable, controlled grade 2 adverse events (AEs) such as peripheral neuropathy, hypothyroidism, hypertension, adrenal insufficiency or alopecia are allowed after discussing with the PI * Patients with known symptomatic, untreated central nervous system (including brain, spinal cord); patients who have a history of brain/central nervous system (CNS) metastasis are eligible for the study provided that all the following criteria are met: * Brain/CNS 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 * History of allergic reactions attributed to compounds of similar chemical or biologic composition to MLN0128 (TAK-228) * Subjects who are on systemic corticosteroids (intravenous (IV) or oral steroids, excluding inhaled, topical or ophthalmic corticosteroids), or anti-epileptic drugs for treated brain metastasis * Subjects taking strong inhibitors and/or inducers of cytochrome P450 (CYP) 3A4, CYP2C19 or CYP2C9 within 1 week preceding the first dose of MLN0128 (TAK-228); if a subject requires treatment with strong inhibitors and/or inducers of CYP3A4, CYP2C19 and/or CYP2C9, alternative treatment must be considered; if no alternative is available, one such medication may be allowed after discussing with the study principle investigator * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia (excluding rate controlled atrial fibrillation/flutter), or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant and breastfeeding women are excluded from this study because fertility and developmental studies with MLN0128 (TAK-228) have not been conducted and there is a potential risk for adverse events including teratogenicity and risk of abortion; breastfeeding should be discontinued if the mother is treated with MLN0128 (TAK-228) * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with MLN0128 (TAK-228); however, HIV patients treated with regimens that have low CYP450 inhibition may be allowed as long as the patient's general health and CD4 counts are within acceptable levels * Patients with 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) * Patients with untreated or active hepatitis B or C infection * 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) * Pulmonary hypertension * Uncontrolled asthma or oxygen (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 * Manifestations of malabsorption due to prior gastrointestinal (GI) surgery, GI disease, or for an unknown reason that may alter the absorption of MLN0128 (TAK-228) * Concomitant administration of any proton pump inhibitor (PPI) is not permitted during the study; patients receiving PPI therapy before enrollment must stop using the PPI for 7 days before their first dose of study drugs * 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 transient ischemic attack (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) * Pulmonary embolism * New York Heart Association (NYHA) class III or IV heart failure * Placement of a pacemaker for control of rhythm * Subjects who have initiated treatment with bisphosphonates less than 30 days prior to the first administration of MLN0128 (TAK-228); concurrent bisphosphonate use is only allowed if the bisphosphonate was initiated at least 30 days prior to the first administration of MLN0128 (TAK-228) * Patients who received prior PI3K, AKT or mTOR inhibitors are not allowed * Patients who received radiation therapy within the last 4 weeks; radiation exposure may not exceed 30% of marrow area