The goal of this clinical research study to find the highest tolerated dose of the combination of Taxotere (docetaxel) and Rapamycin (sirolimus) when given to patients with advanced cancer.

Researchers also want to find highest tolerated dose of the combination of docetaxel, sirolimus, and prednisone when given to patients with advanced prostate cancer. The safety of both drug combinations will also be studied.

The Study Drugs:

Docetaxel is designed to stop the growth of cancer cells, which may cause the cells to die. It is believed to be weakly effective at killing blood vessels in tumor tissue as well.

Sirolimus is designed to block a protein called mammalian target of rapamycin (mTOR) inside the cancer cell.

Prednisone is a corticosteroid that is similar to a natural hormone made by your body. Prednisone is often given in combination with chemotherapy to treat cancer.

Study Groups:

If you are found to be eligible to take part in this study, you will be assigned to a dose level of the combination of docetaxel and sirolimus based on when you joined this study. Up to 12 dose levels of docetaxel and sirolimus will be tested. Three (3) 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 docetaxel and sirolimus is found. Once the highest tolerable dose of docetaxel and sirolimus is found, up to 12 more patients may be enrolled to further study the safety of the drug at each of that dose.

If you have prostate cancer, you will also receive prednisone. All participants who receive prednisone will receive the same dose level.

Study Drug Administration:

Each study cycle is 21 days.

Everyday, you will take sirolimus by mouth 1 time a day. Sirolimus can be taken with or without food, but should be taken at the same time everyday.

On Day 1 of every cycle, you will receive docetaxel by vein over about 1 hour.

If you are taking prednisone, you will take it 2 times every day by mouth with food and water.

Study Visits:

Every week for the first 3 weeks and then about every 3 weeks, blood (about 5 teaspoons) will be drawn for routine tests. You will also have a physical exam.

Every 6 weeks, women who are able to have children will have blood drawn for a pregnancy test.

About every three weeks, blood (about 5 teaspoons) will be drawn for routine tests, to check your kidney function, and for biomarker tests.

About every 6 weeks, you will have a CT scan and x-ray to check the status of the disease.

Length of Study:

You will be on study for as long as you are benefitting. You will be taken off the study if the disease gets worse or you experience intolerable side effects.

Follow-Up:

If you experience intolerable side effects, you will be followed until the side effect has resolved or the side effect does not continue to improve or get worse. The study doctor will tell you what tests will need to be performed.

This is an investigational study. Docetaxel is FDA approved and commercially available for the treatment of advanced cancers such as breast, lung, and prostate cancer. Sirolimus is FDA approved and commercially available for the prevention of transplant rejection in kidney transplant patients. Prednisone is FDA approved and commercially available for the treatment of prostate cancer when given with docetaxel.

The combination of docetaxel and sirolimus, with or without prednisone, to treat advanced cancer is investigational. Most patients in this study will receive docetaxel and sirolimus. However, if you have prostate cancer, you will receive docetaxel, prednisone, and sirolimus.

Up to 68 patients will be enrolled in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients with advanced or metastatic cancer that is refractory to standard therapy, relapsed after standard therapy, or who have no standard therapy available that improves survival by at least three months.
2. Patients must be at least 5 half-lives or three weeks, whichever is shorter, from their previous targeted or biologic therapy; patients must be at least three weeks beyond previous cytotoxic therapy. In addition, patients must be >/= 3 weeks beyond previous therapeutic radiation or major surgery. Patients may have received palliative localized radiation immediately before or during treatment providing radiation is not delivered only to the site of disease being treated under this protocol. Terminal phase half life of docetaxel is 11.1 hours; sirolimus, 14.5 hours.
3. cont'd from criterion #2 Previous mTOR inhibitor (everolimus, temsirolimus, and sirolimus) and taxane (including paclitaxel, abraxane/ABI-007, and docetaxel) therapy is permitted.
4. Eastern Cooperative Oncology Group (ECOG) performance status </= 3
5. Patients must have normal organ and marrow function defined as:absolute neutrophil count >/= 1,000/mL; platelets >/=50,000/mL; creatinine \