Study of Mutation-Targeted Therapy With Sunitinib or Everolimus in People With Advanced Low- or Intermediate-Grade Neuroendocrine Tumors of the Gastrointestinal Tract and Pancreas With or Without Cytoreductive Surgery

-INCLUSION CRITERIA: 1. Progressive, histologically or cytologically diagnosed low or intermediate grade, neuroendocrine tumors confirmed by the Laboratory of Pathology, National Cancer Institute (NCI). Disease progression is defined according to Response Evaluation Criteria in Solid Tumors (RECIST) criteria for progression of disease or any new lesions seen on 68-Gallium DOTATATE within the 18 months prior to enrolment. 2. Age greater than or equal 18 years, because the incidence and prevalence of metastatic pancreatic and gastrointestinal neuroendocrine tumors in the pediatric patient population is exceedingly rare (children are excluded from this study, but will be eligible for future pediatric trials). 3. Patients must have measurable disease according to RECIST criteria on anatomic imaging studies (computed tomography (CT) scan or magnetic resonance imaging (MRI)). 4. Willingness to undergo tumor biopsy if the patient does not have a known familial cancer syndrome (multiple endocrine neoplasia type 1 (MEN1), Von Hippel-Lindau (VHL) and neurofibromatosis type 1 (NF1)). Archival tissue available. 5. Eastern Cooperative Oncology Group (ECOG) performance status \<2. 6. Patients must have normal organ and bone marrow function as defined below: * hemoglobin greater than or equal 9 g/dL \* * leukocytes greater than or equal 3,000/mcL \* * absolute neutrophil count greater than or equal 1,500/mcL \* * platelets greater than or equal institutional lower limit of normal * total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT)/alanine aminotransferase (ALT) serum glutamic-pyruvic transaminase (SGPT) less than or equal 2.5 times institutional upper limit of normal (less than or equal 5 times upper limit of normal (ULN) in patients with liver metastases) \- creatinine within normal institutional limits OR * creatinine clearance greater than or equal 60 mL/min/1.73 m(2) for patients with creatinine levels above institutional normal. * International Normalized Ratio (INR) less than or equal 2; * If a patient's bone marrow function falls below the indicated values and it is not thought to be related to prior treatments a hematology consult will be ordered. If Hematology deems the patients safe to proceed with treatment they will be allowed to enroll on study. In such cases, the patients absolute neutrophil count must be greater than 1,000/mcl, hemoglobin must be greater than 7.5 g/dL and the platelet count must be \> 75,000 mcL. Each patient will also be seen by a medical oncologist at follow-up visits if possible. 7. Fasting serum cholesterol less than or equal 300 mg/dL OR less than or equal 7.75 mmol/L AND fasting triglycerides less than or equal 2.5x ULN. NOTE: In case one or both of these thresholds are exceeded, the patient can only be included after initiation of appropriate lipid lowering medication; 8. Women of childbearing potential (WOCBP) or partners of WOCBP participating in this study must agree to use highly effective contraception while on treatment and for at least 8 weeks after end of treatment, because the effects of Sunitinib and Everolimus on the developing human fetus are unknown. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Highly effective contraception methods include combination of: 1. Any two of the following: * Use of oral, injected or implanted hormonal methods of contraception or; * Placement of an intrauterine device (IUD) or intrauterine system (IUS); * Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/ vaginal suppository; 2. Total abstinence or; 3. Male/female sterilization. Women are considered post-menopausal and not of child-bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks prior to enrollment. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child-bearing potential. 9. Must have fully recovered from toxicities of any prior treatment with cytotoxic drugs, radiotherapy, surgery, or other anti-cancer modalities (returned to baseline status as noted before most recent treatment or less than or equal grade 1). 10. Ability of subject to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: * Uncontrolled hypertension (\>150/100 mmHg). * Prior external beam radiation therapy to the target lesion(s) within 1 months prior to enrollment * Prior systemic chemotherapy or therapy with one of the investigational agents within 1 month prior to enrollment. * Patients who had therapy with one of the investigational agents more than 1 month prior to enrollment in whom tumor genotyping show assignment to the same investigational agent. * Patients who are receiving any other investigational agents. * Patients with known brain metastases will be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to Sunitinib or Everolimus. * Patients who have any severe and/or uncontrolled medical conditions such as: 1. unstable angina pectoris, symptomatic congestive heart failure, myocardial infarction less than or equal 6 months prior to start of Everolimus, serious uncontrolled cardiac arrhythmia, or any other clinically significant cardiac disease 2. symptomatic congestive heart failure of New York heart Association Class III or IV 3. active (acute or chronic) or uncontrolled severe infection, liver disease such as cirrhosis, decompensated liver disease 4. known severely impaired lung function 5. Corrected QT interval (QTc) interval \> 450 msec for males or \> 470 msec for females 6. active, bleeding diathesis; 7. psychiatric illness/social situations that would preclude informed consent, limit compliance with study requirements * Pregnant or nursing patients will be excluded from the study, because the effects of Sunitinib and Everolimus on the developing human fetus are unknown. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with Sunitinib or Everolimus, breastfeeding should be discontinued if the mother is treated with Sunitinib or Everolimus. * Current treatment with therapeutic doses of Coumadin-derivative anticoagulants (low dose Coumadin up to 2 mg by mouth (PO) daily for deep vein thrombosis prophylaxis is allowed). * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with study agents. * Lack of physical integrity of the upper gastrointestinal tract or malabsorption syndrome, or the inability to take oral medication * Uncontrolled diabetes mellitus as defined by hemoglobin A1C (HbA1c) \>8% despite adequate therapy. Patients with a known history or diagnosis of diabetes mellitus who are on therapy and have had good blood sugar control may be included, even if the HbA1c is \> 8% because this value can take up to 3-4 months to normalize * Patients who have received live attenuated vaccines within 1 week of start of Everolimus and during the study. Patient should also avoid close contact with others who have received live attenuated vaccines. Examples of live attenuated vaccines include intranasal influenza, measles, mumps, rubella, oral polio, Bacille Calmette-Guerin (BCG), yellow fever, varicella and TY21a typhoid vaccines * Patients who are on chronic treatment with corticosteroids or other immunosuppressive agents (topical or inhaled corticosteroids are allowed) * Patients with a history of non-compliance to medical regimens or who are considered potentially unreliable or will not be able to complete the entire study * Patients who are taking medications that are strong inhibitors of cytochrome P450 AA4 (CYP3A4) or PgP and need to remain on these medications. For a current table of Substrates, Inhibitors and Inducers please access the following website:http://www.fda.gov/Drugs/DevelopmentApprovalProcess/DevelopmentResourc es/DrugInteractionsLabeling/ucm093664.htm * Patients who have a history of another primary malignancy from which the patient has been disease free for \< 3 years at the time of enrolment, with the exceptions of: a patient with a familial cancer syndrome-associated NETs including MEN1, VHL, NF-1, and tuberous sclerosis (TS);