Inclusion Criteria:

          -  Patient has signed the Informed Consent prior to any screening procedures being
             performed and is able to comply with the protocol requirements.

          -  Adults ≥ 18 years old

          -  Histologic or cytologic diagnosis of a WDNET, Ki67 ≤ 30%, unresectable, of foregut
             origin (thymic, bronchopulmonary, gastric, duodenal, and pancreatic) confirmed by the
             enrolling institution

             *Note: If patients have a functional NET, they are permitted to continue on a
             somatostatin analog for hormonal symptom control

          -  MSK patient has tissue available from a previous biopsy for the evaluation of
             potential predictive biomarkers. If tissue is not available for MSK patient, a new
             tumor specimen will need to be obtained prior to the start of study treatment If
             archived tissue is available, participating site patient will provide for the
             evaluation of potential predictive biomarkers. If tissue is not available for
             participating site patient, a new tumor specimen is optional prior to the start of
             study treatment.

          -  Documented radiological evidence for disease progression (measurable or nonmeasurable)
             ≤12 months prior to enrollment

          -  Disease that is currently not amenable to surgical resection with curative intent as
             determined by the treating investigator

          -  Measurable disease as defined by RECIST v1.1

          -  ECOG performance status 0 or 1 or KPS performance status 100 to 70

          -  Patient has adequate bone marrow and organ function as defined by the following
             laboratory values at screening:

               -  Absolute neutrophil count ≥1.5 x 10^9/L

               -  Platelets ≥ 100 x 10^9/L

               -  Hemoglobin ≥ 9.0 g/dL

               -  INR ≤ 1.5

               -  Serum creatinine <1.5mg/dL or creatinine clearance ≥ 50 mL/min

               -  In the absence of liver metastases, alanine aminotransferase (ALT) and aspartate
                  aminotransferase (AST) <2.5 x ULN. If a patient has liver metastases, ALT and AST
                  <5 x ULN

               -  Total bilirubin < ULN; or total bilirubin ≤3.0 x ULN or direct bilirubin ≤1.5 x
                  ULN in patients with well-documented Gilbert"s Syndrome

          -  Negative serum pregnancy test done ≤14 days prior to registration, for women of
             childbearing potential only A serum pregnancy test will be conducted ≤ 72 hours prior
             to treatment start as a pre-treatment parameter. All women of reproductive potential
             and their partners must agree to use adequate methods of birth control (e.g. latex
             condoms) throughout the study and for 30 days after the last dose of study drug.

             † A female of reproductive potential is a sexually mature female who: has not
             undergone a hysterectomy or bilateral oophorectomy; or has not been naturally
             postmenopausal for at least 24 consecutive months (i.e. has had menses at any time in
             the preceding 24 consecutive months).

          -  Patient with standard 12-lead ECG with the following parameters at screening (defined
             as the mean of the triplicate ECGs)

             °QTcF interval at screening <450msec (using Fridericia"s correction)

          -  Must be able to swallow LEE011 and everolimus capsules/tablets

          -  Recovered from adverse events (to grade 1 or less toxicity according to CTCAE 4.0) due
             to agents administered previously *NOTE: Chemotherapy-induced alopecia and grade 2
             neuropathy are acceptable

        Exclusion Criteria:

          -  Patient has a known hypersensitivity to any of the excipients of LEE011 or everolimus

          -  Previous treatment with a CDK 4/6 inhibitor or an mTOR inhibitor

          -  Has had prior chemotherapy, targeted small molecule therapy within 2 weeks prior to
             study Day 1 or who has not recovered (i.e. ≤ Grade 1 or at baseline) from adverse
             events due to a previously administered agent

             *Note: Subjects with < Grade 2 neuropathy or chemotherapy-induced alopecia are an
             exception to this criterion and may qualify for the study

          -  Patient has a concurrent malignancy or malignancy within 3 years prior to starting
             study drug, with the exception of adequately treated, basal or squamous cell
             carcinoma, non-melanomatous skin cancer or curatively resected cervical cancer

          -  Patients with central nervous system (CNS) involvement unless they meet ALL of the
             following criteria:

               -  At least 4 weeks from prior therapy completion (including radiation and/or
                  surgery) to starting the study treatment

               -  Clinically stable CNS tumor at the time of screening and not receiving steroids
                  and/or enzyme-inducing anti-epileptic medications for brain metastases

          -  Patient has impairment of gastrointestinal (GI) function or GI disease that may
             significantly alter the absorption of the study drugs (e.g., ulcerative diseases,
             uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel
             resection)

          -  Patient has a known history of HIV infection (testing not mandatory)

          -  Patient has any other concurrent severe and/or uncontrolled medical condition that
             would, in the investigator"s judgment, cause unacceptable safety risks, contraindicate
             patient participation in the clinical study or compromise compliance with the protocol
             (e.g. chronic pancreatitis, active untreated or uncontrolled fungal, bacterial or
             viral infections, etc.).

          -  Uncontrolled diabetes mellitus as defined by HbA1c >8% despite adequate therapy.
             Patients with a known history of impaired fasting glucose or diabetes mellitus (DM)
             may be included, however blood glucose and antidiabetic treatment must be monitored
             closely throughout the trial and adjusted as necessary

          -  Clinically significant, uncontrolled heart disease and/or cardiac repolarization
             abnormality, including any of the following:

               -  History of myocardial infarction (MI), angina pectoris, symptomatic pericarditis,
                  or coronary artery bypass graft (CABG) within 6 months prior to study entry

               -  Documented cardiomyopathy

               -  Left Ventricular Ejection Fraction (LVEF) < 50% as determined by Multiple Gated
                  acquisition (MUGA) scan or echocardiogram (ECHO)

               -  Long QT syndrome or family history of idiopathic sudden death or congenital long
                  QT syndrome, or any of the following:

               -  Risk factors for Torsades de Pointe (TdP) including uncorrected hypokalemia or
                  hypomagnesemia, history of cardiac failure, or history of clinically
                  significant/symptomatic bradycardia

               -  Concomitant medication(s) with a known risk to prolong the QT interval and/or
                  known to cause Torsades de Pointe that cannot be discontinued or replaced by safe
                  alternative medication (e.g. within 5 half-lives or 7 days prior to starting
                  study drug)

               -  Inability to determine the QTcF interval

               -  Clinically significant cardiac arrhythmias (e.g., ventricular tachycardia),
                  complete left bundle branch block, high-grade AV block (e.g., bifascicular block,
                  Mobitz type II and third degree AV block)

          -  Patient is currently receiving any of the following medications and cannot be
             discontinued 7 days prior to starting study drug

               -  Known strong inducers or inhibitors of CYP3A4/5, including grapefruit, grapefruit
                  hybrids, pummelos, star-fruit, and Seville oranges, that have a narrow
                  therapeutic window and are predominantly metabolized through CYP3A4/5

               -  Herbal preparations/medications, dietary supplements

          -  Patient is currently receiving or has received systemic corticosteroids ≤2 weeks prior
             to starting study drug, or who have not fully recovered from side effects of such
             treatment

             °The following uses of corticosteroids are permitted: single doses, topical
             applications (e.g., for rash), inhaled sprays (e.g., for obstructive airways
             diseases), eye drops or local injections (e.g., intra-articular)

          -  Participation in a prior investigational study within 30 days prior to enrollment or
             within 5 half-lives of the investigational product, whichever is longer

          -  Patient who has received radiotherapy ≤4 weeks or limited field radiation for
             palliation ≤2 weeks prior to starting study drug, and who has not recovered to grade 1
             or better from related side effects of such therapy (exceptions include alopecia) or
             in whom ≥25% of the bone marrow (Ellis, 1961) was irradiated

          -  Patient has had major surgery within 14 days prior to starting study drug or has not
             recovered from major side effects (tumor biopsy is not considered as major surgery)

          -  Patient with a Child-Pugh score B or C

          -  Patient has a history of non-compliance to medical regimen or inability to grant
             consent

          -  Pregnant or nursing (lactating) women, where pregnancy is defined as the state of a
             female after conception until the termination of gestation, confirmed by a positive
             hCG laboratory test.