Everolimus in Patients With Advanced Solid Malignancies With TSC1, TSC2, NF1, NF2, or STK11 Mutations

Inclusion Criteria: * Histologically confirmed diagnosis of advanced (metastatic, recurrent, or unresectable) cancer with mutations in any of the following genes: TSC1, TSC2, NF1, NF2 or STK11. * Must have failed at least 1 standard of care systemic therapy for their malignancy * Measurable disease defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>10 mm with CT scan, as \>20 mm by chest x-ray, or \>10 mm with calipers by clinical exam. * Prior therapy (chemotherapy, radiation therapy, and surgery) is allowed if completed at least 2 weeks prior to registration and if all treatment-related toxicities are resolved to ≤ CTCAE grade 1, with the exception of alopecia and hematologic values otherwise meeting the bone marrow function criteria specified below. * At least 18 years of age. * ECOG performance status ≤ 2 * Normal bone marrow and organ function as defined below: * Leukocytes \> 3,000/mcL * Absolute neutrophil count \> 1,500/mcL * Platelets \> 100,000/mcL * Hemoglobin \> 9.0 g/dL * Total serum bilirubin ≤ 2.0 x IULN * AST(SGOT)/ALT(SGPT) ≤ 2.5 x IULN (≤ 5.0 x IULN in patients with liver metastases) * Serum creatinine ≤ 1.5 x IULN OR creatinine clearance \> 45 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Fasting cholesterol ≤ 300 mg/dL OR ≤ 7.75 mmol/L AND fasting triglycerides ≤ 2.5 x IULN. NOTE: In case one or both of these thresholds are exceeded, the patient can only be included after initiation of appropriate lipid lowering medication * Able to swallow tablets. * Women of childbearing potential, defined as all women physiologically capable of becoming pregnant, must use highly effective methods of contraception during the study and for 8 weeks after. Women are considered post-menopausal and not of childbearing 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 randomization. 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 childbearing potential. * Male patients whose sexual partner(s) are women of childbearing potential must agree to use adequate contraception during the study and for 8 weeks after the end of treatment. * Able to understand and willing to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable) Exclusion Criteria: * A history of other malignancy ≤ 3 years previous with the exception of basal cell or squamous cell carcinoma of the skin which were treated with local resection only or carcinoma in situ of the cervix. * Taking an investigational agent within 4 weeks of initiation of everolimus. * Symptomatic brain metastases. Known brain metastases are allowed if asymptomatic and previously treated. * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to everolimus or other agents used in the study. * Known impairment of GI function or GI disease that may significantly alter the absorption of oral everolimus. * Currently taking CYP3A4 inhibitors or inducers (such as the antiepileptic drugs phenytoin, carbamazepine, or phenobarbital; cyclosporine; grapefruit or its juice; Seville oranges; starfruit; or St. John's wort) * Chronic treatment with corticosteroids or other immunosuppressive agents. Topical or inhaled corticosteroids are allowed. * Received live attenuated vaccine within 1 week of start of everolimus (i.e. intranasal influenza, measles, mumps, rubella, oral polio, BCG, yellow fever, varicella, and TY21a typhoid vaccines). * Uncontrolled diabetes mellitus defined as HbA1c \> 8% despite adequate therapy. Patients with a known history of impaired fasting glucose or diabetes mellitus may be included; however, blood glucose and antidiabetic treatment must be monitored closely throughout the trial and adjusted as necessary. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure of NYHA class III or IV, active coronary artery disease, unstable angina pectoris, cardiac arrhythmia, myocardia infraction ≤ 6 months prior to start of everolimus, uncontrolled hypertension (systolic pressure \> 150 mmHg or diastolic pressure \> 90 mmHg), uncontrolled seizure disorder, liver disease such as cirrhosis, decompensated liver disease, active and chronic hepatitis, known severely impaired lung function (spirometry and DLCO 50% or less of normal and 02 saturation 88% or less at rest on room air), active bleeding diathesis, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant and/or breastfeeding. Women of childbearing potential must have a negative pregnancy test within 14 days of study entry. * Known HIV-positivity on combination antiretroviral therapy because of the potential for pharmacokinetic interactions with everolimus. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated.