The goal of this clinical research study is to find the highest tolerable dose of carfilzomib that can be given to patients with lymphoma after a stem cell transplant. The safety of this drug will also be studied.

Carfilzomib is designed to block cancer cells from repairing themselves. If the cancer cells cannot repair themselves, this may cause them to die.

Study Groups:

If you agree to take part in this study, you will be assigned to a dose level of carfilzomib based on when you joined this study. Up to 4 dose levels of carfilzomib will be tested. Three (3) participants will be enrolled at each dose level until the highest tolerable dose level is found. Each new group will receive a higher dose than the group before it, if no intolerable side effects were seen. When the highest tolerable dose is found, more participants may be enrolled at that dose level.

Study Treatment:

Each study cycle is 28 days.

On Days 1, 2, 15, and 16 of each cycle, you will receive carfilzomib by vein over 30 minutes. You will receive hydration by vein before and after each infusion of carfilzomib in Cycle 1. This may be repeated in Cycle 2, if your doctor thinks it is needed. On these days during Cycles 1 and 2, before you receive carfilzomib you will receive dexamethasone by vein or as a tablet by mouth. Dexamethasone may help prevent possible infusion reactions. You may continue to receive dexamethasone before each dose of each cycle depending how well you tolerate the infusion.

You will be monitored closely for at least 1 hour for possible infusion reactions after each dose during Cycle 1 and on Day 1 of Cycle 2. If you have an infusion reaction, your doctor may delay or stop the infusion, and you may receive drugs to help relieve the symptoms.

You will have about 12 days of "rest" between each cycle of treatment (during this time you will not receive carfilzomib).

Study Visits:

On Day 1 (+ or - 3 days) of Cycle 1 and on Day 1 of all other cycles, women who are able to become pregnant will have blood (about 1 teaspoon) drawn for a pregnancy test. To take part in this study, you must not be pregnant.

About 1 day before you receive carfilzomib in each cycle:

• You will have a physical exam including measurement of your vital signs (blood pressure, heart rate, temperature, and breathing rate).
• You will be asked about how you are feeling and about any side effects you may be having.

About 1 day and about 15 days before you receive carfilzomib in each cycle, blood (about 2 tablespoons) will be drawn for routine tests and to check your kidney and liver function.

At any point that your doctor thinks they are needed, you will have a bone marrow aspiration and computed tomography (CT) and/or positron emission tomography (PET) scans to check the status of the disease. To collect a bone marrow aspirate, an area of the hip or other site is numbed with anesthetic, and a small amount of bone marrow is withdrawn through a large needle.

End-of-Treatment Visit:

Within 30 days of your last dose of study drug, you will return to the clinic. The following tests and procedures will be performed:

• You will have a physical exam, including measurement of your vital signs.
• You will be asked about how you are feeling and about any side effects you may be having.
• Blood (about 4 tablespoons) will be drawn for routine tests and to check the status of the disease.

During follow-up, the study staff may also contact you and your local doctor by telephone to ask about your health.

Length of Study:

You may remain in this study for about 2 years from the time of first dose. You may receive up to 6 cycles of treatment during this time, which will take about 7 months to complete. You will be taken off study early if the disease gets worse, you cannot keep appointments, you miss more than 2 doses of carfilzomib in a row, if intolerable side effects occur, or if you decide that you want to leave the study early.

This is an investigational study. Carfilzomib is FDA approved and commercially available for the treatment of multiple myeloma. The use of carfilzomib to treat lymphoma after a stem cell transplant is investigational.

Up to 30 participants will be enrolled in this study. All will take part at MD Anderson.

Inclusion Criteria:

1. Patients with mantle cell lymphoma, T-cell lymphoma, and diffuse large b-cell lymphoma within 6 months post autologous transplantation and without relapse.
2. Age >/= 18 years to </= 70 years.
3. Absolute neutrophil count (ANC) >/= to 1.5 x 10^9/L; Platelets > 75 x 10^9/L.
4. No active infection.
5. Performance status: Eastern Cooperative Oncology Group (ECOG) 2 or less or Karnofsky of at least 60.
6. Cardiac EF >/= 45% by 2D-Echo.
7. Serum creatinine less than 1.6 mg/dl and Creatinine Clearance >/= to 30 mL/min.
8. Liver function tests less than 2x upper limit of normal range (unless related to medications or Gilbert's disease).
9. Females of childbearing potential who are not pregnant or breastfeeding.
10. Patient or legally authorized representative able to sign informed consent.

Exclusion Criteria:

1. Glucocorticoid therapy (prednisone >30 mg/day or equivalent within 14 days of first dose.
2. POEMS syndrome.
3. Plasma cell leukemia or circulating plasma cells >/= 2 X 10^9/L.
4. Waldenstrom's Macroglobulinemia.
5. Patients with known amyloidosis.
6. Immunotherapy or chemotherapy with approved or investigational anticancer therapeutics within 21 days of first dose.
7. Patients previously randomized in any other Onyx-sponsored Phase 3 trial.
8. Active congestive heart failure (NYHA Class III to IV), symptomatic ischemia, or conduction abnormalities uncontrolled by conventional intervention. Myocardial infarction within 6 months.
9. Acute active infection requiring systemic antibiotics, antiviral (except antiviral directed at Hepatitis B) or antifungal agents within 14 days of first dose.
10. Known HIV seropositive, hepatitis C infection, and/or hepatitis B (except for patients with hepatitis B SAg or core antibody receiving and responding to antiviral therapy directed at hepatitis B: these patients are allowed).
11. Patients with known cirrhosis.
12. Second malignancy within past three years except: a. adequately treated basal or squamous cell skin cancer. b. carcinoma in situ of the cervix. c. prostate cancer < Gleason Score 6 with stable prostatic specific antigen (PSA) over the past three months. d. breast cancer in situ with full surgical resection. e. treated medullary or papillary thyroid cancer.
13. Patients with myelodysplastic syndrome.
14. Significant neuropathy (Grades 3 to 4, or Grade 2 pain).
15. Known hypersensitivity to carfilzomib.
16. Known contraindication to dexamethasone.
17. Pleural effusions requiring thoracentesis or ascites requiring paracentesis within 14 days of first dose.
18. Any other clinically significant medical disease or psychiatric condition that, in the Investigator's opinion, may interfere with protocol compliance.