Neratinib With and Without Temsirolimus for Patients With HER2 Activating Mutations in Non-Small Cell Lung Cancer

Inclusion Criteria 1. Aged ≥18 years at the time of signing the informed consent. 2. Histologically confirmed diagnosis of NSCLC, advanced (stage IIIB) or metastatic (stage IV). 3. Documented somatic ErbB2 (HER2) activating mutation. 4. Patients with anaplastic lymphoma kinase (ALK) translocations must have received crizotinib, except for cases of intolerable toxicity to crizotinib. 5. At least one measurable lesion as defined by Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST v1.1). 6. Eastern Cooperative Oncology Group (ECOG) status \<2. 7. Left ventricular ejection fraction (LVEF) ≥50% measured by multiple -gated acquisition scan (MUGA) or echocardiogram (ECHO). 8. Negative β-human chorionic gonadotropin (hCG) pregnancy test for premenopausal women of reproductive capacity (those who are biologically capable of having children) and for women less than 12 months after menopause. 9. Men and women of childbearing potential must agree and commit to the use of a highly effective method of contraception, as determined to be acceptable by the Investigator, from the time of informed consent until 3 months after the last dose of the investigational products. 10. Provide written, informed consent to participate in the study and follow the study procedures. Exclusion Criteria 1. Previous treatment with any investigational agent ≤14 days prior to the initiation of investigational products. 2. Previous treatment with any strong inhibitor and/or inducer of CYP3A4 enzyme or sensitive P-glycoprotein (P-gp) substrates ≤30 days prior to the initiation of investigational products. 3. Active uncontrolled cardiac disease, including cardiomyopathy, congestive heart failure (New York Heart Association functional classification of ≥2), unstable angina, myocardial infarction within 12 months of enrollment, or ventricular arrhythmia. 4. Major surgery \<30 days of starting treatment. 5. Chronic steroid use (prednisone \>12.5 mg/day or dexamethasone \>2 mg/day, excluding inhaled steroids). 6. Currently breast feeding. 7. Symptomatic or unstable brain metastases. 8. QTc interval \>0.450 seconds for men and \>0.470 seconds for women, or known history of QTc prolongation or Torsades de Pointes (TdP). 9. Significant chronic gastrointestinal disorder with diarrhea as a major symptom (e.g., Crohn's disease, malabsorption, or Grade ≥2 (National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events Version 4.0 \[CTCAE v.4.0\] diarrhea of any etiology at baseline). 10. Prior exposure to neratinib or mTOR inhibitor. 11. Active infection or unexplained fever \>38.5°C (101.3°F). 12. Unable or unwilling to swallow tablets. 13. Evidence of significant medical illness, abnormal laboratory finding, or psychiatric illness/social situations that would, in the Investigator's judgment, make the patient inappropriate for this study. 14. Known hypersensitivity to any component of the investigational products. 15. Unstable or uncontrolled diabetes mellitus (glycosylated hemoglobin \[HbA1c\] \>6.5%). 16. Screening laboratory assessments outside the following limits: ANC \<1000/μL (\<1.0 x 109/L), Platelet count \<75,000/μL (\<75 x 109/L), Hemoglobin \<8 g/dL, transfusions allowed, must be at least 7 days prior to baseline, Total bilirubin \>1.5 x institutional upper limit of normal (ULN), AST and/or ALT 5 minutes, Creatinine clearance \<50 mL/min.