The goal of this clinical research study is to learn the highest safe doses of the combination of Doxil (liposomal doxorubicin), Avastin (bevacizumab), and Torisel (Temsirolimus) that can be given to patients with advanced cancer that has spread or is unable to be surgically removed. The safety and effectiveness of this combination of drugs will also be studied.

The Study Drugs:

Liposomal doxorubicin is designed to cause cancer cells to be fragile, which may cause the cancer cells to die.

Bevacizumab is designed to block or slow down the growth of cancer cells by blocking the growth of blood vessels that supply nutrients for tumor growth.

Temsirolimus is designed to block the growth of cancer cells, which may eventually cause the cancer cells to die.

Everolimus is designed to block a protein called mammilian target of rapamycin (mTOR) inside the cancer cells, which is involved in cancer cell growth.

Study Groups:

If you are found to be eligible to take part in this study, you will be assigned to a fixed dose level of a combination of liposomal doxorubicin, bevacizumab, and either temsirolimus or everolimus, based on when you joined this study. Up to 9 dose levels of the study drug combination will be tested. Three (3) 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 the study drug combination is found.

Study Drug Administration:

Liposomal doxorubicin, bevacizumab, and either temsirolimus or everolimus will be given in "cycles." Cycles will be about 21 days (or longer, depending on any side effects you may experience).

Liposomal doxorubicin is given by vein on Day 1 of each cycle. On Day 1 of Cycle 1, you will receive it over 3 hours. If you tolerate it well in Cycle 1, you will receive it over 60 minutes in Cycle 2. If you tolerate it well in Cycle 2, you will receive it over 60 minutes for all further cycles.

Bevacizumab is given by vein on Day 1 of each cycle. On Day 1 of Cycle 1, you will receive it over 90 minutes. If you tolerate it well in Cycle 1, you will receive it over 60 minutes in Cycle 2. If you tolerate it well in Cycle 2, you will receive it over 30 minutes in Cycle 3. It will continue to be given over 30 minutes in Cycle 4 and further cycles, as long as you still tolerate it well.

Temsirolimus is given by vein on Days 1, 8, and 15 of each cycle. During Day 1 of Cycle 1, you will receive it over 60 minutes. If you tolerate it well on Day 1 of Cycle 1, it will be given over 30 minutes on Days 8 and 15 of Cycle 1 and over 30 minutes in further cycles, as long you still tolerate it well.

Everolimus works the same way and has been shown to be as effective as temsirolimus. Everolimus can also be given by mouth, so it can be substituted for temsirolimus. Everolimus will be taken every day, starting with Day 1 of Cycle 1.

Because of a nationwide shortage of liposomal doxorubicin, you may only receive temsirolimus and bevacizumab until liposomal doxorubicin becomes available.

If you experience certain side effects, your dose level may be lowered. In some cases, your dose may be stopped for 1 week, until the side effect gets better. Your doctor can explain this to you in more detail, if it happens.

Study Visits:

During Cycle 1, you will have a physical exam once and blood will be drawn weekly (about 1 tablespoon) for routine tests.

For Cycle 2 and further cycles, you will have a physical exam and blood drawn (about 1 tablespoon) for routine tests once every 3 weeks.

The status of the disease will be checked by a CT or MRI scan after every 2 cycles, for Cycles 2-6, then every 2-3 cycles.

Additional Procedures for Some Participants:

If you are in the group that receives the highest safe dose of the study drugs, you will have the following additional procedures performed:

• You will have a biopsy performed at the end of Cycle 1. The biopsy will be used for research to see how the study drug combination acts in the body and to learn how it may affect cancer cells.
• You will have a DCE-MRI scan at 24-48 hours after your first study drug infusion (Cycle 1), and at the end of Cycle 1. These DCE-MRI scans will be used for research to see how the study drug combination is affecting blood vessels that supply nutrients and oxygen to tumor cells.

Length of Study Participation:

You may continue to receive additional cycles of the study drugs, unless the cancer goes away completely, gets worse, or if intolerable side effects occur. In that case, you will be taken off study.

Long-Term Follow-Up:

After your last dose of the study drug, you will receive up to 3 phone calls from the study staff. The calls will be 1 month apart, and you will be asked how you are doing.

This is an investigational study. Liposomal doxorubicin, bevacizumab, and temsirolimus are commercially available. Liposomal doxorubicin is FDA approved for the treatment of multiple myeloma, ovarian cancer that has returned, and Kaposi's sarcoma. Bevacizumab is FDA approved for the treatment of colorectal cancer and a type of lung cancer. Temsirolimus is FDA approved for the treatment of kidney cancer that has spread.

The combination of liposomal doxorubicin, bevacizumab, and temsirolimus is not FDA approved. At this time, it is only being used in research.

Up to 206 patients will take part 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 has no standard therapy that improves survival by at least three months.
2. All patients must have an estimated life expectancy of at least 12 weeks.
3. Patients must have measurable or evaluable disease
4. Patients must have been off previous chemotherapy or radiotherapy for the three weeks prior to entering this study. Six weeks will be required if the patient has received therapy which is known to have delayed toxicity (mitomycin or a nitrosurea). Five half-lives will be required for biologic/targeted therapies with short (<24 hour) half-lives and pharmacodynamic effects. Patients may have received palliative radiation immediately before (or during) treatment provided radiation is not to the only target lesion available.
5. Eastern Cooperative Oncology Group (ECOG) performance status </= 2 (Karnofsky >/= 60%).
6. Patients must have organ and marrow function defined as: absolute neutrophil count >/= 1,500/mL; platelets >/=100,000/mL; creatinine </= 3 X upper limit of normal (ULN); total bilirubin </= 2.0; ALT(SGPT) </= 5 X ULN. In patients with significant liver disease and chronically elevated liver transaminases, ALT may be elevated as high as 8 X ULN.
7. Cardiac ejection fraction >/= 50% without evidence of congestive heart failure (CHF).
8. Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 90 days after the last dose.
9. Ability to understand and the willingness to sign a written informed consent document.
10. Patients may not be receiving any other investigational agents and/or any other concurrent anticancer agents or therapies except hormonal maintenance treatment for prostate cancer.

Exclusion Criteria:

1. Patients with clinically significant unexplained bleeding within 28 days prior to entering the study
2. Poorly controlled systemic vascular hypertension (Systolic blood pressure > 140 mmHg, diastolic blood pressure > 90 mmHg)
3. Patients with clinically significant cardiovascular disease: - History of cerebral vascular accident (CVA) within 6 months - Myocardial infarction or unstable angina within 6 months - Unstable angina pectoris - New York Heart Association Class CHF score ≥ II
4. Prior cumulative doxorubicin dose > 300 mg/m2
5. Pregnant or lactating women
6. History of hypersensitivity to doxil, doxorubicin, HCL, temsirolimus or it's metabolites (including sirolimus), polysorbate 80, bevacizumab or murine products
7. Serious medical or psychiatric illness likely to interfere with participation in this clinical study
8. Patients < 12 years of age
9. Inability to swallow tablets for everolimus arm.