The goal of this clinical research study is learn if carfilzomib can help control kidney cancer. 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 and Study Drug Administration:

If you are found to be eligible to take part in this study, you will receive carfilzomib 2 days a week for the first 3 weeks of each 4-week study cycle (Days 1, 2, 8, 9, 15, and 16 of each cycle). Each dose is given by vein over about 30 minutes.

Before you receive the study drug, you will be given dexamethasone to help decrease the risk of side effects during the first cycle. You may ask the study staff for information about how the drugs are given and their risks.

During Cycle 1, you will receive extra fluid (saline) by vein before each dose of study drug. This is part of standard clinical care. This will also be done during Cycle 2, if the study doctor thinks it is needed.

You will remain in the clinic for an extra hour after receiving each dose during Cycle 1 and after the first dose of Cycle 2, to receive additional fluids by vein.

If you have any side effects from the drug, tell the study doctor right away. The study doctor may then lower the dose or keep the dose level the same.

Each study cycle is 4 weeks.

Study Visits:

Weeks 1, 2, and 3 of each cycle:

• Your vital signs and weight will be measured.
• Blood (about 3 teaspoons) will be drawn for routine tests

Every 4 weeks (+/-4 days):

• Your medical history will be recorded.
• You will have a physical exam, including measurement of your vital signs and weight.
• You will be asked about any drugs or treatments you may be receiving and any side effects that you have had.
• Your performance status will be recorded.
• Blood (about 3 teaspoons) will be drawn for routine tests and to check your blood sugar level and your pancreatic function, if the study doctor thinks it is needed. You will be asked to fast (not eat, and drink only water) for at least 8 hours before this blood draw.

Every 8 weeks (+/-7 days):

• You will have an x-ray of chest, CT scan of the chest and abdomen, and MRI scan of the brain to check the status of the disease. If the doctor thinks it is needed, you will also have a bone scan.
• If you can become pregnant, you will have a blood (about 2 teaspoons) pregnancy test.

Length of Study:

You may continue taking the study drug for as long as the doctor thinks it is in your best interest. You will no longer be able to take the study drug if the disease gets worse, intolerable side effects occur, or you are not able to follow study directions.

End-of-Treatment Visit:

About 30 days after your last dose of the study drug:

• You will have a physical exam, including measurement of your vital signs and weight.
• You will be asked about any drugs or treatments you may be receiving and any side effects that you have had.
• Blood (about 3 teaspoons) will be drawn for routine and blood sugar tests.
• You will have an x-ray, CT scan, and MRI scan to check the status of the disease.

Long-Term Follow-up:

After you stop taking the study drug, the study staff will check your health status every 6 months for the rest of your life. The study staff will collect this information by either checking your medical record, emailing you, or calling you on the telephone. Each call should only last about 5 minutes.

This is an investigational study. Carfilzomib is FDA approved and commercially available in treatment of multiple myeloma. The use of carfilzomib in kidney cancer is investigational.

Up to 40 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Biopsy proven clear cell kidney cancer with metastatic disease. Progressive disease or intolerance to at least one but not more than three (3) prior systemic therapy(ies)
2. Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as >/= 20 mm with conventional techniques or as >/= 10 mm with spiral CT scan.
3. Age >/= 18 years
4. Eastern Cooperative Oncology Group (ECOG) performance status 0-2
5. Adequate hepatic function with serum ALT and AST </= 3.0 times the upper limit of normal and serum direct and total bilirubin </= 1.5 times the upper limit of normal.
6. Absolute neutrophil count (ANC) >/= 1.0 × 10^9/L; patients with an ECOG performance status of 2 at study entry must have an ANC >/= 1.5 x 10^9/L
7. Hemoglobin >/= 8 g/dL (80 g/L) within 14 days prior to beginning study treatment (subjects may be receiving red blood cell [RBC] transfusions in accordance with institutional guidelines); Patients with an ECOG performance status of 2 at study entry must have a hemoglobin >/= 9 g/dL (transfusion assistance acceptable)
8. Platelet count >/= 50 × 10^9/L; Patients with an ECOG performance status of 2 at study entry must have a platelet count >/= 100 × 10^9/L
9. Creatinine clearance (CrCl) >/= 30 mL/minute, either measured or calculated using a standard formula (eg, Cockcroft and Gault)
10. Written informed consent in accordance with federal, local, and institutional guidelines.
11. Females of childbearing potential (FCBP) must agree to ongoing pregnancy testing and to practice contraception during the study and for a period of 6 weeks after you stop receiving the study drug
12. Male subjects must agree to practice contraception during the study and for a period of 6 weeks after you stop receiving the study drug

Exclusion Criteria:

1. Brain metastases not controlled with surgery, whole brain radiotherapy, or with stereotactic radiosurgery
2. Systemic therapy within two weeks of treatment initiation
3. Pregnant or lactating females
4. Major surgery within 21 days prior to beginning study treatment
5. Acute active infection requiring treatment (systemic antibiotics, antivirals, or antifungals) within 14 days prior to beginning study treatment
6. Known human immunodeficiency virus infection
7. Active hepatitis B or C infection
8. Unstable angina or myocardial infarction within 4 months prior to beginning study treatment, NYHA Class III or IV heart failure, uncontrolled angina, history of severe coronary artery disease, severe uncontrolled ventricular arrhythmias, sick sinus syndrome, or electrocardiographic evidence of acute ischemia or Grade 3 conduction system abnormalities unless subject has a pacemaker
9. Uncontrolled hypertension (defined by BP consistently > 150/100) or uncontrolled diabetes (defined by HbA1c > 8.5) within 14 days prior to beginning study treatment
10. Nonhematologic malignancy within the past 2 years with the exception of a) adequately treated basal cell carcinoma, squamous cell skin cancer, or thyroid cancer; b) carcinoma in situ of the cervix or breast; c) prostate cancer of Gleason Grade 6 or less with stable prostate-specific antigen levels; or d) cancer considered cured by surgical resection or unlikely to impact survival during the duration of the study, such as localized transitional cell carcinoma of the bladder or benign tumors of the adrenal or pancreas
11. Significant neuropathy (Grades 3-4, or Grade 2 with pain) within 14 days prior to beginning study treatment
12. Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib)
13. Contraindication to any of the required concomitant drugs or supportive treatments, including hypersensitivity to all anticoagulation and antiplatelet options, antiviral drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment
14. Subjects with pleural effusions requiring thoracentesis or ascites requiring paracentesis within 14 days prior to beginning study treatment
15. Any other clinically significant medical disease or condition that, in the Investigator's opinion, may interfere with protocol adherence or a subject's ability to give informed consent

Adverse events will be followed for 30 days beyond discontinuation of treatment for any reason; duration of treatment up to 4 months. All-Cause Mortality will be assessed up to 15 months.