The purpose of this study is to test a new drug called carfilzomib. It is a type of drug called a proteasome inhibitor. Proteasome breaks down proteins that are no longer useful to the cell. When the proteasome is turned off by a drug (like carfilzomib), useless proteins cannot be broken down. Instead the proteins build up and cause the cell to die. Myeloma cells make a lot of protein and are especially in need of a functional proteasome to survive.

Carfilzomib is not approved for use by the Food and Drug Administration to treat myeloma. It is considered an experimental drug. Previous studies have shown that carfilzomib is safe to use. This study will look at what the effects, good and/or bad, carfilzomib has on myeloma.

Inclusion Criteria:

• Participants must meet all of the following inclusion criteria to be eligible to enroll in this study.
• Patients meeting the criteria for symptomatic multiple myeloma that has relapsed or is refractory to at least 2 prior lines of therapy.
• Previous therapy with bortezomib.
• Previous therapy with thalidomide or lenalidomide.
• Patients must have measurable disease and therefore must have at least one of the following:

Serum M-protein ≥1 gm/dL (≥10 gm/L) Urine M-protein ≥200 mg/24 hr Serum FLC assay: involved FLC ≥10 mg/dL (≥100 mg/L) provided serum FLC ratio is abnormal.

• Age ≥ 18 years
• Eastern Cooperative Oncology Group (ECOG) performance status 0-2 Adequate hepatic function, with serum ALT ≤ 3.5 times the upper limit of normal and serum direct bilirubin ≤ 2 mg/dL (34 µmol/L) within 14 days prior to enrollment
• Absolute neutrophil count (ANC) ≥ 1.0 × 109/L within 14 days prior to enrollment Hemoglobin ≥ 8 g/dL (80 g/L) within 14 days prior to enrollment (participants may be receiving red blood cell [RBC] transfusions in accordance with institutional guidelines)
• Platelet count ≥ 50 × 109/L (≥ 30 × 109/L if thought to be secondary to myeloma involvement of the bone marrow ) within 14 days prior to enrollment (platelet transfusions are allowed)
• Creatinine clearance (CrCl) ≥ 15 mL/minute within 14 days prior to enrollment, either estimated or calculated using a standard formula (eg, Cockcroft and Gault)
• Females of childbearing potential (FCBP) must agree to ongoing pregnancy testing and to practice contraception.
• Male participants must agree to practice contraception.

Exclusion Criteria:

• Prior treatment with carfilzomib.
• Known CNS involvement with myeloma
• Pregnant or lactating females
• Major surgery within 21 days prior to registration.
• Acute active infection requiring treatment (systemic antibiotics, antivirals, or antifungals) within 7 days prior to enrollment
• Known human immunodeficiency virus infection
• Active hepatitis B or C infection
• Unstable angina or myocardial infarction within 4 months prior to enrollment, NYHA Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, sick sinus syndrome, or electrocardiographic evidence of acute ischemia or Grade 3 conduction system abnormalities unless participant has a pacemaker
• Uncontrolled hypertension or uncontrolled diabetes within 14 days prior to enrollment.
• Concurrent malignancies, except for treated non-melanoma skin cancer and cervical carcinoma in situ.
• Significant neuropathy (Grades 3-4, ) within 14 days prior to enrollment
• Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib)
• Contraindication to any of the required concomitant drugs or supportive treatments, including options, antiviral drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment
• Concurrent therapy with any other anticancer therapeutic with activity against multiple myeloma
• Concurrent therapy with investigative agents (e.g., antibiotics or antiemetics)