The goal of this clinical research study is to find the highest tolerable dose of the combination of Yervoy® (ipilimumab) with Revlimid® (lenalidomide) that can be given to patients with advanced cancer. The safety of these drugs will also be studied.

Ipilimumab is designed to increase the immune system's ability to fight cancer.

Lenalidomide is designed to change the body's immune system. It may also interfere with the development of tiny blood vessels that help support tumor growth. This may decrease the growth of cancer cells.

Study Groups:

Dose escalation:

If you are found to be eligible to take part in this study, you will be assigned to a dose level of the study drugs based on when you join the study.

Up to 5 dose levels of ipilimumab with lenalidomide will be tested. Up to 6 participants will be enrolled at each dose level. The first group of participants will receive the lowest dose level. Each new group will receive a higher dose than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of ipilimumab with lenalidomide is found.

Dose expansion:

Once the highest tolerable dose of ipilimumab with lenalidomide is found, up to 14 more participants may be enrolled. This will be to further study the safety of the combination of drugs at that dose and the level of effectiveness of the study drugs in a certain tumor group. This group will be called the dose expansion group.

Study Drug Administration:

Each study cycle is 28 days.

You will take lenalidomide by mouth on Days 1-21 of each cycle. You will swallow the capsules whole with water once a day. Do not break, chew, or open your capsules. The doctor will discuss this with you.

You will receive ipilimumab by vein over 90 minutes on Day 1 of each cycle. You will be monitored for side effects for 1-2 hours after the infusion.

Study Visits:

Every study visit:

° You will be asked if you have had any side effects.

Cycle 1:

• On Day 1: blood (about 4 teaspoons) will be drawn for routine tests.
• Between Days 2 and 7: If you are able to become pregnant, you will have a blood (about 1 teaspoon) or urine pregnancy test.
• Between Days 8 and 14: Blood (about 4 teaspoons) will be drawn for routine tests. If you are able to become pregnant, you will have a blood (about 1 teaspoon) or urine pregnancy test.
• Between Days 15 and 21: Blood (about 4 teaspoons) will be drawn for routine tests. If you are able to become pregnant, you will have a blood (about 1 teaspoon) or urine pregnancy test.
• Between Days 22 and 28: Blood (about 4 teaspoons) will be drawn for routine tests. Your medical history will be recorded.

Cycle 2:

• On Day 1: Blood (about 4 teaspoons) will be drawn for routine tests.
• On Day 8 (+/- 3 days): Blood (about 4 teaspoons) will be drawn for routine tests.
• On Day 15 (+/- 3 days): Blood (about 4 teaspoons) will be drawn for routine tests.
• On Day 22 (+/- 3 days): Blood (about 4 teaspoons) will be drawn for routine tests.

Every other cycle (every 8 weeks):

° You will have an x-ray, CT scan, and/or PET/CT scan to check the status of the disease. ° Blood (about 1 tablespoon) will be drawn for tumor marker testing.

Before starting Cycle 3 and all following cycles:

• Your medical history will be recorded.
• You will have a physical exam, including measurement of your weight and vital signs.
• You will be asked about any health problems you may have and any other drugs or herbal supplements you may be taking.
• Your performance status will be recorded.
• Blood (about 4 teaspoons) will be drawn for routine tests. Blood may be drawn more often if your doctor thinks it is needed.
• If you are able to become pregnant, you will have a blood (about 1 teaspoon) or urine pregnancy test.

At the End of the study:

• Directly at the end of the study: If you are able to become pregnant, you will have a blood (about 1 teaspoon) or urine pregnancy test.
• 28 days after therapy with lenalidomide stopped: If you are able to become pregnant, you will have a blood (about 1 teaspoon) or urine pregnancy test.

Length of Dosing:

You may receive up to 4 doses of ipilimumab. You may continue receiving lenalidomide for as long as the doctor thinks it is in your best interest. You will no longer be able to take the study drugs if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions.

You will be off study after your follow-up visit.

Follow-up:

You will have a follow-up-visit within 30 days after your last dose of study drugs. You will be asked about any health problems you may have and if you have had any side effects. If your study doctor thinks it is needed, you may have follow-up for a longer period of time. If you are able to become pregnant, you will have a blood (about 1 teaspoon) or urine pregnancy test.

This is an investigational study. Ipilimumab is FDA approved and commercially available to treat metastatic melanoma. Lenalidomide is FDA approved and commercially available to treat multiple myeloma and myelodysplastic syndrome. Giving the combination of ipilimumab and lenalidomide to patients with advanced cancer is investigational.

Up to 101 patients will be enrolled in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients with advanced or metastatic cancers with no available standard therapy are eligible to enter the Phase 1 portion of this study.
2. Patients must be >/= 18 years.
3. Patients must be >/= 3 weeks beyond treatment with a cytotoxic chemotherapy regimen, or therapeutic radiation, or major surgery. A confirmation (written or verbal) that there is no risk of surgical complications from a patient's surgeon has to be obtained prior to starting therapy in patients with a history of major surgery within past 6 weeks. Patients may have received palliative localized radiation immediately before or during treatment provided that radiation is not delivered to the only site of disease being treated under this protocol. For biologic/targeted agents patients must be >/= 5 half-lives or >/= 3 weeks form the last dose (whichever comes first).
4. ECOG performance status </= 2.
5. Patients must have adequate organ and marrow function defined as: absolute neutrophil count >/= 1,000/mL platelets >/=50,000/mL; CrCl >/=60mL/min by Cockcroft -Gault calculation; total bilirubin \