Inclusion Criteria:

          -  Cytopathologically or histologically confirmed dx of multiple myeloma

          -  Relapsed or refractory to the most recently received therapy.

          -  All pts must have received prior lenalidomide therapy and been determined to be
             refractory, relapsed, or intolerant.

          -  Measurable disease, as indicated by one or more of the following:

        Serum M-protein ≥ 0.5 g/dL Urine Bence Jones protein ≥ 200 mg/24 hr Elevated Free Light
        Chain as per IMWG criteria, and abnormal ratio

          -  Pts must be ≥ 18 years of age

          -  Life expectancy of more than 3 months

          -  ECOG PS of 0-2

          -  Adequate hepatic function, with bilirubin < 2 times the upper limit of normal (ULN),
             and aspartate aminotransferase (AST) and alanine aminotransferase (ALT) < 3 times ULN

          -  Uric acid must be within laboratory normal range

          -  CrCl ≥ 50 mL/min

          -  Additional Laboratory Requirements ANC ≥1.0 x 109/L Hgb ≥8 g/dL(transfusion permitted)
             Platelet count ≥50.0 x 109/L

          -  Screening ANC should be independent of granulocyte-and granulocyte/macrophage colony
             stimulating factor (G-CSF and GM-CSF) support for at least 1 week and of pegylated
             G-CSF for at least 2 weeks

          -  Pts may receive RBC or platelet transfusions, if clinically indicated, in accordance
             with institutional guidelines

          -  Screening platelet count should be independent of platelet transfusions for at least 2
             weeks.

          -  Written informed consent in accordance with federal, local, and institutional
             guidelines

          -  FCBP must agree to ongoing pregnancy testing

          -  FCBP must have a negative serum or urine pregnancy test and agree to birth control.

          -  Male pts must agree to never have unprotected sexual contact with a female who can
             become pregnant and must agree to either completely abstain from sexual contact with
             females who are pregnant or are able to become pregnant. The patient must agree to
             inform his physician if he has had unprotected sexual contact with a female who can
             become pregnant or if he thinks for any reason that his sexual partner may be
             pregnant.

          -  Male pts cannot donate semen or sperm while taking pomalidomide and for 28 days after
             completing the study.

          -  All pts must be counseled at a minimum of every 28 days about pregnancy precautions
             and risks of fetal exposure.

          -  Pts must agree to take enteric-coated aspirin 81 mg orally daily, or if history of
             prior thrombotic disease, must be fully anticoagulated with warfarin (INR 2-3) or be
             treated with full-dose, low molecular weight heparin, as if to treat deep venous
             thrombosis (DVT)/pulmonary embolism (PE)at the investigator's discretion

        Exclusion Criteria:

          -  Pts with known sensitivity to any immunomodulatory drugs (IMiDs)

          -  Use of any other experimental drug or therapy within 21 days prior to first dose

          -  Exposure to any prior chemotherapy, steroid use, or other myeloma treatment within 14
             days prior to first dose. Pts currently on long term steroids do not require any
             washout period. in addition, steroid use for spinal cord compression is permitted and
             does not require a washout period.

          -  Radiation therapy within 14 days prior to first dose

          -  Known allergies to carfilzomib or Captisol

          -  POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and
             skin changes)

          -  Current diagnosis of plasma cell leukemia

          -  Waldenström's macroglobulinemia

          -  Major surgery within 21 days prior to first dose

          -  Pregnant or lactating females

          -  Congestive heart failure (NYHA class III to IV), symptomatic ischemia, conduction
             abnormalities uncontrolled by conventional intervention or myocardial infarction in
             the previous six months prior to first dose.

          -  Uncontrolled hypertension

          -  Acute active infection requiring systemic antibiotics, antivirals, or antifungals
             within 14 days prior to first dose

          -  Pts receiving active treatment or intervention for any other malignancy or pts who, at
             the Investigator's discretion, may require active treatment or intervention for any
             other malignancy within 8 months of starting study treatment.

          -  Serious psychiatric or medical conditions that could interfere with treatment

          -  Significant neuropathy (Grade 3, Grade 4, or Grade 2 with pain) at the time of the
             first dose and/or within 14 days before enrollment

          -  Contraindication to any of the required concomitant drugs, including proton-pump
             inhibitor (e.g. lansoprazole), enteric-coated aspirin or if a history of prior
             thrombotic disease, warfarin or low molecular weight heparin

          -  Pts in whom the required program of oral and intravenous fluid hydration is
             contraindicated, e.g. due to pre-existing pulmonary, cardiac, or renal impairment

          -  Pts with primary systemic amyloidosis

          -  Pts who have received prior treatment with carfilzomib (Phase II only)

          -  Pts who have received prior treatment with pomalidomide (Phase II only)

          -  Pts who have received prior treatment with both carfilzomib & pomalidomide (Phase I
             only)