Inclusion Criteria:

          -  This trial has two step inclusion criteria.

        Step 1 Inclusion Criteria

          1. Male or female patients 18 years or older.

          2. Patients must have a diagnosis of a locally advanced or metastatic sarcoma that is
             progressing. The following subtypes (considered genomically complex) will be eligible:
             leiomyosarcoma (well differentiated or poorly differentiated), undifferentiated
             pleomorphic sarcoma, myxofibrosarcoma, pleomorphic rhabdomyosarcoma, pleomorphic
             liposarcoma, malignant peripheral nerve sheath tumor, angiosarcoma or extraskeletal
             osteosarcoma. Other potentially genomically complex Soft Tissue Sarcomas (STS)
             subtypes may be included on a case-by-case basis after discussion with the principal
             investigator.

          3. Measurable disease by RECIST 1.1 criteria (at least one target lesion outside of
             previous radiation fields or progressed within a previous radiation field), described
             in detail in section 15.

          4. Progression of disease by radiographic imaging (10% increase in size by RECIST v1.1
             within 6 months of registration) or presence of new lesions.

          5. Must have received at least 1 prior systemic therapy for advanced disease (does not
             include adjuvant/neoadjuvant therapy in a curative setting).

          6. Eastern Cooperative Oncology Group (ECOG) performance status 0-2.

          7. Adequate contraception as follows:

             For women:

             Postmenopausal for at least 1 year before the screening visit, OR Surgically sterile,
             OR If they are of childbearing potential, agree to practice 1 effective method of
             contraception, and 1 additional (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. United Surgical Partners Internationals (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 (Periodic abstinence [e.g, calendar, ovulation, symptothermal, postovulation
             methods] and withdrawal, spermicides only, and lactational amenorrhea are not
             acceptable methods of contraception. Female and male condoms should not be used
             together.)

             Highly effective methods:

             Intra-uterine devices (IUD) Hormonal (birth control pills/oral contraceptives,
             injectable contraceptives, contraceptive patches, or contraceptive implants)

             Other effective Methods:

             Latex Condoms Diaphragm with spermicide; Cervical cap;Sponge

             For men, even if surgically sterilized (ie, status post-vasectomy), they 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 (Periodic abstinence [e.g, calendar, ovulation, symptothermal,
             postovulation methods for the female partner] and 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 120 days after receiving
             their last dose of study drug

          8. Screening clinical laboratory values as specified below:

             a) Bone marrow reserve consistent with: i. absolute neutrophil count (ANC) ≥ 1.5 x
             10(9)/L; ii. platelet count ≥ 100 x 10(9)/L; iii. hemoglobin ≥ 9 g/dL without
             transfusion within 1 week preceding study drug administration b) Hepatic: i. total
             bilirubin ≤ 1.5 x upper limit of normal (ULN), ii. 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 Cockcroft-Gault estimate or based on urine collection (12 or 24 hour); d)
             Metabolic: i. Glycosylated hemoglobin (HbA1c) ≤ 7.0%, ii. fasting serum glucose ≤ 130
             mg/dL iii. fasting triglycerides ≤ 300 mg/dL

          9. Ability to swallow oral medications.

         10. 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.

         11. Patients who have a history of brain metastasis are eligible for the study provided
             that all the following criteria are met:

               1. Brain metastases which have been treated

               2. No evidence of disease progression for ≥ 3 months or hemorrhage after treatment

               3. Off-treatment with dexamethasone for 4 weeks before administration of the first
                  dose of TAK-228

               4. No ongoing requirement for dexamethasone or anti-epileptic drugs

        Step 2 Inclusion Criteria: Must be met after meeting step1inclusion and exclusion criteria.

        1. Tumor must have dysregulation of the PI3K/AKT/mTOR pathway. For the purposes of this
        study, patients must have either PTEN protein or genomic loss, or
        phosphatidylinositol-4,5-bisphosphate 3-kinase, catalytic subunit alpha (PIK3CA)/
        Phosphatase and tensin homolog (PTEN) mutation. Patients must be willing to provide
        sufficient archival tissue. If this is not available fresh tumor for biopsy is required. In
        the event that a patient has had tumor analyzed for PTEN/PIK3CA status through commercial
        means, their eligibility and need for additional tissue will be determined on a case by
        case basis by the principle investigator.

        Exclusion Criteria:

          -  Step 1 Exclusion Criteria

               1. Any 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.

               2. Known human immunodeficiency virus infection.

               3. Known hepatitis B surface antigen-positive, or known or suspected active
                  hepatitis C infection.

               4. Any serious medical or psychiatric illness that could, in the investigator's
                  opinion, potentially interfere with the completion of treatment according to this
                  protocol.

               5. 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.

               6. Breast feeding or pregnant.

               7. 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.

               8. Treatment with any investigational products, radiation therapy, surgery, tumor
                  embolization, chemotherapy or immunotherapy within 21 days before the first dose
                  of the study drug. For biologic or hormonal therapy treatment within 14 days or
                  five half-lives of a drug (whichever is longer) before the first dose of study
                  drug.

               9. History of any of the following within the last 6 months before administration of
                  the first dose of the drug:

                    1. Ischemic myocardial event, including angina requiring therapy and artery
                       revascularization procedures

                    2. Ischemic cerebrovascular event, including transient ischemic attack and
                       artery revascularization procedures

                    3. Requirement for inotropic support (excluding digoxin) or serious
                       (uncontrolled) cardiac arrhythmia (including atrial flutter/fibrillation,
                       ventricular fibrillation or ventricular tachycardia)

                    4. Placement of a pacemaker for control of rhythm

                    5. New York Heart Association (NYHA) Class III or IV heart failure

                    6. Pulmonary embolism

              10. Significant active cardiovascular or pulmonary disease including:

                    1. Uncontrolled hypertension (i.e., systolic blood pressure >180 mm Hg,
                       diastolic blood pressure >95 mm Hg). Use of anti-hypertensive agents to
                       control hypertension before Cycle1 Day 1 is allowed.

                    2. Pulmonary hypertension

                    3. Uncontrolled asthma or O2 saturation < 90% by arterial blood gas analysis or
                       pulse oximetry on room air

                    4. Significant valvular disease; severe regurgitation or stenosis by imaging
                       independent of symptom control with medical intervention, or history of
                       valve replacement

                    5. Medically significant (symptomatic) bradycardia

                    6. History of arrhythmia requiring an implantable cardiac defibrillator

                    7. 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)

              11. Poorly controlled diabetes mellitus defined as glycosylated hemoglobin (HbA1c)
                  >7% ; patients with a history of transient glucose intolerance due to
                  corticosteroid administration or gestational diabetes may be enrolled in this
                  study if all other inclusion/exclusion criteria are met.

              12. Treatment with strong inhibitors and/or inducers of cytochrome P450 (CYP) 3A4,
                  CYP2C19 or CYP2C9 within 1 week preceding the first dose of study drug.

              13. Patients receiving systemic 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.

              14. 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.