The goal of this clinical research study is to find the highest safe dose of the drug Velcade (bortezomib) that can be given together with gemcitabine and pegylated liposomal doxorubicin (Doxil) in the treatment of advanced cancer. The effect of this combination treatment on tumor growth will also be studied.

Pegylated liposomal doxorubicin is a newer form of the common anticancer drug Adriamycin. It is enclosed in liposomes, which are fat particles found normally in the body. This new form is designed to act against cancer cells while causing less damage to normal tissue. Gemcitabine is a drug that has shown to be active in patients with several different cancers including pancreatic cancer, breast cancer, and certain lymphomas. Bortezomib is a new drug that is designed to block the proteins needed for tumor growth.

Groups of 3 participants that are less than 65 years old and 3-6 participants that are at least 65 years old will be enrolled at a time. Each new group will receive a higher dose level than the group before as long as no serious side effects occur.

Once the highest tolerable dose is determined, up to 30 additional patients with small cell cancer or neuroendocrine carcinoma, and up to 30 patients with T cell lymphoma will be treated at that dose.

All participants will receive pegylated liposomal doxorubicin through a vein over about 2 hours. The drug will be given once every 21 days (3 weeks or 1 cycle). Gemcitabine will be given through a vein over 30 minutes on Days 1 and 8 every 21 days. Patients will only receive the combination of both drugs on Day 1; on that day pegylated liposomal doxorubicin will be given before the dose of gemcitabine. Bortezomib will be given by vein on Days 1, 4, 8 and 11 of every 21 days, except for the first group of patients who will receive it on days 1 and 8 only. Participants whose tumors are responding to treatment may continue treatment if their doctor approves for as long as they respond, as long as there are no serious side effects.

Because of a nationwide shortage of pegylated liposomal doxorubicin, you may continue treatment with gemcitabine and bortezomib. If pegylated liposomal doxorubicin becomes available, you may be able to receive it again.

During the study, you will have a weekly blood test (about 2 tablespoons of blood) and a physical exam. X-rays and other scans, such as MRIs and CT scans, will be done at 6 weeks to measure the size of the tumor. Other tests will be done if needed.

The treatment will be stopped if the cancer grows or if severe side effects occur, and other treatments may be offered.

This is an investigational study. All three drugs are approved by the FDA for use against some kinds of cancer. Their use in this study is investigational. Up to 276 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. All patients with histologic proof of advanced cancer, who are not candidates for known regimens or protocol treatments of higher efficacy or priority or who have no therapy that increases survival by at least 3 months, shall be eligible for this study unless the standard therapy includes one or more of the drugs in this protocol.
2. Estimated life expectancy of at least 12 weeks. (Performance status of less than or equal to 2 (Zubrod scale).
3. Patients must voluntarily sign an informed consent indicating that they are aware of the investigational nature of this study in keeping with the policies of the hospital. The only acceptable consent form is the one attached at the end of this protocol.
4. Evaluable disease
5. Patients must have been off all previous chemotherapy or radiotherapy for at least 3 weeks and off all targeted biologic therapies for at least 5 half-lives, whichever is shorter, prior to entering this study. Patients may receive localized palliative radiotherapy immediately before or during treatment.
6. Adequate bone marrow function (Absolute neutrophil count (ANC) > 1,500 and Platelet > 100,000) except in the post-transplant arm where the hematologic minimum requirements will not apply if there is disease infiltration of the bone marrow.
7. Adequate liver function (bilirubin of less than or equal to 1.5 mg%, alanine aminotransferase (SGPT) < 5 times normal)
8. Adequate renal function (creatinine less than or equal to 1.5 mg%).
9. Cardiac ejection fraction greater than or equal to 50% without evidence of Congestive heart failure (CHF)
10. Female subject is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intrauterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study.
11. Male subject agrees to use an acceptable methods for contraception of the duration of the study.

Exclusion Criteria:

1. Symptomatic brain metastases requiring concurrent treatment, inclusive of but not limited to, surgery, radiation or cortico steroids.
2. Need for concurrent radiotherapy or other chemotherapy (other than localized palliative radiotherapy)
3. New York Heart Association Class > II
4. Diagnosis of leukemia or myelodysplastic syndrome
5. Prior cumulative doxorubicin dose > 300 mg/m^2. Total cumulative dose of doxorubicin plus Doxil should not exceed 550 mg/m^2 (or 400 mg/m)
6. Pregnant or lactating women. Confirmation that the subject is not pregnant must be established by a negative serum beta-human chorionic gonadotropin (beta-hCG) pregnancy test result obtained during screening.
7. Patient has greater than or equal to Grade 2 peripheral neuropathy within 14 days before enrollment
8. Concurrent uncontrolled infection requiring intravenous antibiotics
9. Patient has hypersensitivity to bortezomib, boron, mannitol, doxorubicin, or gemcitabine.
10. Patient has received other investigational drugs within 14 days before enrollment.
11. Serious medical or psychiatric illness likely to interfere with participation in this clinical study.