The goal of this clinical research study is to find the highest tolerable dose of LDE225 that can be given in combination with everolimus to patients with esophageal or GEJ cancer. The safety of the drug combination will also be studied.

Study Groups:

If participant is found to be eligible to take part in this study, participant will be assigned to a combination dose level of the study drugs based on when participant joins this study. Up to 6 participants will be enrolled at each dose level. The first group of participants will receive the lowest dose level of LDE225. Each new group will receive a higher dose than the group before it, if no intolerable side effects were seen. All participants will receive the same dose level of everolimus. This will continue until the highest tolerable combination dose of LDE225 and everolimus is found. Up to 24 participants will be enrolled in this part of the study.

Once the highest tolerable dose of the combination of LDE225 and everolimus is found, up to 18 participants will receive the combination dose level that was found to be well tolerated in the earlier part of the study.

Study Drug Administration:

Every study cycle is 28 days.

Participant will take up to 4 capsules or tablets of LDE225 by mouth 1 time every day. Participant's doctor will tell participant how many capsules/tablets participant will need to take. Participant should take the study drug each time with a glass of water (about 8 ounces total) at the same time every day. Participant should swallow the study drug whole, one capsule/tablet every 2 minutes, without chewing or opening the study drug. Participant should eat a light breakfast (such as toast and jam) at least 2 hours before taking the study drug, then participant should not eat or drink anything for at least 1 hour after the dose.

Participant will take up to 2 tablets of everolimus by mouth 1 time every day with the LDE225 capsules without food. Participant will take the tablets each time with a glass of water at the same time every day. The tablets should be swallowed whole and not chewed or crushed.

If participant cannot swallow the everolimus tablets, the tablets should be dissolved in water just before taking them. Add about 2 tablespoons of water into a glass. The tablets should then be added and stirred gently until the tablets are dissolved. This mixture should then be drunk. Afterwards, the glass should be rinsed with an additional 2 tablespoons of water and drunk. Participant's doctor will discuss this with participant.

If participant vomits after taking participant's dose of study drugs, participant should not take another dose that day.

It is very important that participant takes the study drugs given to participant just as the study doctor tells participant and that participant does not miss any dose. If participant forgets to take a dose of LDE225, participant should take it as soon as participant remembers (within 6 hours of the missed dose). If more than 6 hours have passed, participant should skip that dose and take participant's next dose the next day as planned. If participant forgets to take a dose of everolimus, participant should skip that dose and take participant's next dose the next day as planned.

If participant has a study visit that day, participant should take participant's dose of study drugs at the clinic.

Participant will need to store LDE225 in participant's refrigerator at all times. Everolimus can be stored at room temperature. Participant should not share participant's supply of LDE225 and everolimus with anyone. Participant will keep a study drug diary to help participant keep track of participant's study drug doses. If participant misses or delays a dose, participant should write it down in the diary. Participant should bring the diary to every study visit.

At the end of each cycle and when participant stops taking part in the study, participant will return any leftover study drugs to the study nurse.

Study Visits:

On Day 1 of every cycle:

• Participant will have a physical exam.
• Blood (about 2 teaspoons) will be drawn for routine tests.
• If participant can become pregnant, blood (about 1 teaspoon) or urine will be collected for a pregnancy test.

Every week during Cycle 1 only, the study staff will call and ask participant how participant is doing.

On Day 1 of Cycle 2 and every 2 cycles after that, participant will have an EKG.

On Day 1 of Cycle 3 and every 2 cycles after that, participant will have a CT scan or MRI of the chest, abdomen, and pelvis to check the status of the disease.

If the doctor thinks it is needed, extra blood may be drawn to follow up on any side effects.

Length of Study:

Participant may continue taking the study drugs for as long as the doctor thinks it is in participant's best interest. Participant will no longer be able to take the study drugs if the disease gets worse, if intolerable side effects occur, or if participant is unable to follow study directions.

Participation on the study will be over after the follow-up visit (described below).

End-of-Study Visit:

Within 14 days after participant's last dose of study drugs:

• Participant will have a physical exam.
• Blood (about 2 tablespoons) will be drawn for routine tests, to check the cholesterol levels in participant's blood, and to check how well participant's blood clots. Participant will need to fast for at least 8 hours before this blood draw.
• Participant will have an EKG.
• Participant will have a CT scan or MRI of the chest, abdomen, and pelvis to check the status of the disease, if the doctor thinks it is needed.
• If participant can become pregnant, blood (about 1 teaspoon) or urine will be collected for a pregnancy test.

Follow-Up Visit:

At 30 days after the end-of-study visit:

• Participant will have a physical exam.
• Blood (about 2 tablespoons) will be drawn for routine tests.
• Participant will have an EKG.
• If participant can become pregnant, blood (about 1 teaspoon) or urine will be collected for a pregnancy test.

About 3 months after the follow-up visit, participant will be contacted by the study staff by telephone and/or seen in the clinic. Participant will be asked about any drugs participant may be taking and about participant's general health. If participant is called, the call will take about 5-10 minutes.

This is an investigational study. LDE225 is not FDA approved or commercially available. Everolimus is FDA approved and commercially available to treat kidney, breast, and pancreatic cancers. The combination of LDE225 and everolimus to treat esophageal or GEJ cancer is investigational.

The study doctor can explain how the study drugs are designed to work.

Up to 42 participants will be enrolled in this study. All will take part at MD Anderson.

Inclusion Criteria:

1. Patients must have histologically or cytologically confirmed adenocarcinoma of esophagus,gastroesophageal junction, or stomach which is Gli-1 positive (labeling index [LI] greater than or equal to 5%). Testing is to be performed in a CLIA certified laboratory. The patients must have an archival tumor sample to facilitate this testing.
2. Patients must have an unresectable locally advanced or metastatic adenocarcinoma.
3. Patients agreeing to the optional biomarker study in the expansion phase only need to have an accessible primary tumor. (Optional biomarker studies will be done in up to 18 patients in the expansion phase only.)
4. Patient must have received at least one, and no more than two prior systemic therapies for metastatic cancer.
5. Patients whose esophageal or GEJ cancer has become metastatic or unresectable locally advanced within 6 months of completing definitive therapy for localized or locally advanced cancer can be considered as having received one line of therapy for advanced cancer.
6. Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as greater than 20 mm with conventional techniques or as greater than 10 mm with spiral CT scan.
7. Male or female patients greater than or equal to 18 years old.
8. ECOG performance status less than 2.
9. Patients must have normal organ and marrow function as defined below: leukocytes greater than 3,000/mcL; absolute neutrophil count greater than1,500/mcL; platelets greater than 100,000/mcL; Hemoglobin (Hgb) greater than or equal to 9 g/dL (transfusions are allowed); total bilirubin within normal institutional limits; AST(SGOT)/ALT(SGPT) less than 2.5 x institutional upper limit of normal (ULN) or less than or equal to 5 x institutional ULN if liver metastasis are present; Serum creatinine less than or equal to 1.5 x ULN or 24-hour clearance greater than or equal to 50ml/min; Plasma creatine phosphokinase (CK) less than 1.5 x ULN; INR less than or equal to 2; Fasting serum cholesterol less than or equal to 300 mg/dL OR less than or equal to 7.75 mmol/L AND fasting triglycerides less than or equal to 2.5 x ULN.
10. Patient should be able to swallow and retain oral medications.
11. Women of childbearing potential and men must use two forms of contraception (non-hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation and for 6 months after the final dose of study treatment.
12. Ability to understand and the willingness to sign a written informed consent document. Signed informed consent will be obtained prior to any screening procedures.

Exclusion Criteria:

1. Patients currently receiving anticancer therapies or who have received anticancer therapies within 4 weeks of the start of Everolimus and LDE225 (including chemotherapy, radiation therapy, antibody based therapy, etc.).
2. Uncontrolled diabetes mellitus as defined by HbA1c greater than 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.
3. Patients who have any severe and/or uncontrolled medical conditions such as: a) unstable angina pectoris, symptomatic congestive heart failure, myocardial infarction less than or equal to 6 months prior to start of Everolimus, serious uncontrolled cardiac arrhythmia, or any other clinically significant cardiac disease; b) symptomatic congestive heart failure of New York Heart Association Class III or IV; c) active (acute or chronic) or uncontrolled severe infection, liver disease such as cirrhosis, decompensated liver disease, and chronic hepatitis (i.e. quantifiable HBV-DNA and/or positive HbsAg, quantifiable HCV-RNA); d) known severely impaired lung function (spirometry and DLCO 50% or less of normal and O2 saturation 88% or less at rest on room air); e) active, bleeding diathesis.
4. Patients who have a history of another primary malignancy, with the exceptions of: non-melanoma skin cancer, and carcinoma in situ of the cervix, uteri, or breast from which the patient has been disease free for greater than or equal to 3 years.
5. 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.
6. Pregnant or nursing (lactating) women.
7. Women of child-bearing potential (WOCBP), defined as all women physiologically capable of becoming pregnant, must use highly effective methods of contraception during the study and 6 months after. Hormonal contraception methods (e.g. oral, injected, implanted) are not allowed as it cannot be ruled out that the study drug decreases the effectiveness of hormonal contraception. Highly effective contraception methods include combination of any two of the following: a) Placement of a non-hormonal intrauterine device (IUD) or non-hormonal intrauterine system (IUS); b) Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/ vaginal suppository; c. Total abstinence (When this is in line with the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception.);
8. (Continued from # 7): or d) Male/female sterilization. (Sterilization: Patient has had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment. Male partner sterilization (with the appropriate post-vasectomy documentation of the absence of sperm in the ejaculate). [For female study patients, the vasectomized male partner should be the sole partner for that patient.]).
9. (Continued from # 8): 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 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 child-bearing potential.
10. Male patients whose sexual partner(s) are WOCBP who are not willing to use adequate contraception, during the study and for 6 months after the end of treatment (Male patients must use highly effective (double barrier) methods of contraception (e.g., spermicidal gel plus condom) for the entire duration of the study, and continuing using contraception and refrain from fathering a child for 6 months following the study drug. A condom is required to be used also by vasectomized men as well as during intercourse with a male partner in order to prevent delivery of the study treatment via seminal fluid.).
11. Patients with known brain metastases should 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.
12. History of allergic reactions attributed to compounds of similar chemical or biologic composition to LDE 225 or Everolimus in the study or other rapamycin analogs (e.g. sirolimus, temsirolimus).
13. Patients who are receiving treatment with medications known to be moderate and strong inhibitors or inducers of CYP3A4/5 or drugs metabolized by CYP2B6 or CYP2C9 that have narrow therapeutic index, and that cannot be discontinued before starting treatment with LDE225. Medications that are strong CYP3A4/5 inhibitors should be discontinued at least 7 days and strong CYP3A/5 inducers for at least 2 weeks prior to starting treatment with LDE225.
14. Patients receiving any medications or substances that are inhibitors or inducers of CYP 450 3A4 are ineligible.
15. Patients who have neuromuscular disorders (e.g. inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis and spinal muscular atrophy) or are on concomitant treatment with drugs that are recognized to cause rhabdomyolysis, such as HMG CoA inhibitors (statins), clofibrate and gemfibrozil, and that cannot be discontinued at least 2 weeks prior to starting LDE225 treatment. Patients who are planning on embarking on a new strenuous exercise regimen after initiation of study treatment, should also be excluded. Muscular activities, such as strenuous exercise, that can result in significant increases in plasma CK levels should be avoided whilst on LDE225 treatment.
16. Concurrent medical condition requiring the use of immunosuppressive medications or immunosuppressive doses of systemic or absorbable topical corticosteroids (doses greater than 10mg/day prednisone or equivalent). Inhaled or intranasal corticosteroids (with minimal systemic absorption) may be continued. Non-absorbed intra-articular steroid injections are allowed. The exception to the use of steroids is the treatment of serious adverse events (SAEs) such as pneumonitis and the prevention of emesis.
17. Known history of HIV seropositivity.
18. Patients who have received live attenuated vaccines within 1 week of start of Everolimus and during the study.
19. Impaired cardiac function or clinically significant heart disease, including any one of the following: a) Angina pectoris within 3 months; b) Acute myocardial infarction within 3 months; c) QTcF greater than 450 msec for males and greater than 470 msec for females on the screening electrocardiogram (ECG); d) A past medical history of clinically significant ECG abnormalities or a family history of prolonged QT-interval syndrome; e) Other clinically significant heart disease (e.g. congestive heart failure, uncontrolled hypertension, history of labile hypertension, or history of poor compliance with an antihypertensive regimen).
20. All patients known to be positive for hepatitis B will be excluded from the study, and those at high risk for hepatitis B infection will be screened.