This is an open-label, cohort study to determine the feasibility and tolerability of the combination of TAK-228 and TAK-117 given on days 2-4, 9-11, 16-18, and 23-25 with paclitaxel on days 1, 8, and 15 for one 28-day cycle in patients with advanced solid tumors.

The goal of this study is to determine a tolerated dose of the combination of TAK-228, TAK-117 and paclitaxel. To do this, investigators will estimate the maximum tolerated dose that is defined as the dose level at which less than one-third of patients will experience a dose-limiting toxicity. A traditional dose escalation design will be used, beginning with the lowest dose level and escalating to the maximum allowable dose level as specified in the protocol. Three patients will be treated one at a time at a given dose level. A maximum of 5 dosing levels results in a maximum sample size of n=30 subjects. Adverse events will be defined using the Common Toxicity Criteria v. 4.0. dose-limiting toxicity is defined as:

• Grade 3 or higher nonhematologic toxicity, despite adequate treatment, except for the following:

  • Grade 3 hyperglycemia lasting ≤14 days (all patients should receive optimal antiglycemic treatment, including insulin, as clinically indicated).
  • Grade 3 rash lasting ≤3 days (all patients should receive topical steroid treatment, oral antihistamines, and oral steroids, if necessary).
  • Inadequately treated Grade 3 nausea and/or vomiting and Grade 3 diarrhea (all patients should receive optimal antiemetic and/or antidiarrheal prophylaxis and/or treatment).

• Grade 4 neutropenia lasting >7 days in the absence of growth factor support.

• Grade 4 neutropenia of any duration accompanied by fever ≥38.5°C and/or systemic infection.

• Any other ≥Grade 4 hematologic toxicity.

• Inability to administer at least 75% of planned doses of TAK-228 within Cycle 1, due to study drug-related toxicity.

• Any clinically significant occurrence that the investigator and sponsor agree would place patients at an undue safety risk.

Patients experiencing any grade 3 or more hematologic toxicity attributed to the treatment will hold all therapy until resolution of the toxicity to grade 2 or less. If toxicity persists, the patients will be removed from the study. Upon resolution of the toxicity, the patient will restart treatment at the original dose at the discretion of the investigators.

One of the following outcomes will determine the treatment of subsequent patients:

• If none of the three patients experiences a dose-limiting toxicity, the next group of patients will be entered in the next higher dose cohort. All patients within a cohort must have completed at least once cycle (28 days) prior to initiation of the next cohort of patients.
• If one of the three patients experiences a dose-limiting toxicity, three more patients will be accrued at the current dose level. Subsequently, if only one of the six patients treated at this level experiences a dose-limiting toxicity, the dose will be escalated to the next higher dose in the next group of patients. If two or more of the six patients experiences a dose-limiting toxicity, the maximum tolerated dose has been exceeded and is defined as the previous dose at which no more than 1/3 experienced a dose-limiting toxicity.
• If at least two of the three experience a dose-limiting toxicity, the maximum tolerated dose has been exceeded and is defined as the previous dose at which no more than 1/3 experienced a dose-limiting toxicity.

If the lowest allowable dose level exceeds the maximum tolerated dose, the study will be terminated and the combination will not be deemed safe for use in this population. Additionally, the highest dose level will not be exceeded, even if no dose-limiting toxicities are experienced at that dose.

The adverse events overall and by individual adverse events categories will be summarized. Serious adverse events will be summarized in a similar manner. These summaries will be performed overall and for each dose cohort. Investigators will summarize all events as well as the highest grade for a given subject. Investigators will summarize the number of subjects that exhibit a dose-limiting toxicity at each dose cohort and describe the dose-limiting toxicity for each subject, if applicable.

Inclusion Criteria:

• Male or female patients 18 years or older

• Patients must have a diagnosis of an advanced solid tumor malignancy and must be refractory to or intolerant of existing therapies known to provide a clinical benefit

• Eastern Cooperative Oncology Group (ECOG) performance status and/or other performance status of 0-2

• 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 must have a negative pregnancy test and agree to practice one effective method of pregnancy prevention 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 [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, sympto- thermal and post ovulation 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, sympto- thermal and post ovulation 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

• 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 Cockcroft-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

• Ability to swallow oral medications

• Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that the patient may withdraw consent at any time without prejudice to future medical care

• 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

Exclusion Criteria:

• Active central nervous system (CNS) metastasis
• Other clinically significant co-morbidities, in the opinion of the investigators, 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
• Known human immunodeficiency virus infection
• Known hepatitis B surface antigen-positive, or known or suspected active hepatitis C infection.
• Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol
• 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.
• Breast feeding or pregnant
• Treatment with any investigational products within 30 days before the first dose of study drug
• Previous treatment with PI3K, AKT, dual PI3K/mTOR inhibitors, TORC1/2 inhibitors (prior treatment with everolimus is allowed)
• 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 small bowel or jejunal stomata are also excluded.

Serious Adverse Events and Other (Not Including Serious) Adverse Events were collected up to 27 months. All-Cause Mortality was collected up to 43 months.

At each visit the investigator had to document any occurrence of adverse events and abnormal laboratory findings. Any event spontaneously reported by the participant or observed by the investigator was recorded, irrespective of the relation to study treatment.