Phase I/II Trial of the Combination of Lenalidomide (Revlimid) and Nab-paclitaxel (Abraxane) in the Treatment of Relapsed/Refractory Multiple Myeloma

Inclusion Criteria: * Patients with relapsed/refractory multiple myeloma based on standard criteria * Renal function assessed by calculated creatinine clearance as follows * Phase I subjects must have calculated creatinine clearance \>=30ml/min by Cockcroft-Gault formula. * Phase II subjects must have calculated creatinine clearance \>=30ml/min by Cockcroft-Gault formula. * Progressed (\>25% increase in evaluable disease) or non response on Revlimid or within 60 days of stopping Revlimid * \> 1 prior regimen * Total bilirubin \<=1.5 x Upper limit of normal (ULN) * AST (aspartate aminotransferase) or serum glutamic-oxaloacetic transaminase (SGOT) and alanine aminotransferase (ALT) or serum glutamic-pyruvic transaminase (SGPT) \<=3 x ULN. * All study participants must be registered into the mandatory Revlimid REMS® program, and be willing and able to comply with the requirements of Revlimid REMS®. * Females of childbearing potential must have a negative serum or urine pregnancy test with a sensitivity of at least 50 mIU/mL (milli-International unit/milliliter) within 10 - 14 days and again within 24 hours prior to prescribing lenalidomide for Cycle 1 (prescriptions must be filled within 7 days as required by Revlimid REMS) and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME, at least 28 days before she starts taking lenalidomide. * Able to take aspirin (81 or 325 mg) daily as prophylactic anticoagulation (patients intolerant to ASA (acetylsalicylic acid) may use warfarin or low molecular weight heparin). * With \< or = grade 2 neuropathy * Karnofsky performance status ≥ 50 * Patients treated with local radiotherapy with or without a brief (2 weeks or less) exposure to steroids are eligible. Patients who require concurrent radiotherapy should have entry to the protocol deferred until the radiotherapy is completed * Meets the following pretreatment laboratory criteria at Baseline (Day 1 of Cycle 1, before study drug administration) 1. Platelet count ≥ 75 x 10\^3/uL (upper limit) . 2. Hemoglobin ≥ 8.0 g/dL (grams/deciliter) 3. Absolute neutrophil count ≥ 1.0 x 10\^3/uL * Age 18 years or older Exclusion Criteria: * \> grade 2 neuropathy * \> Cr (complete response) 2.5 * LFTs (liver function test) \> 2x nl (normal limit) * Patient had myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any ECG (electrocardiogram) abnormality at screening must be documented by the investigator as not medically relevant. * Known hypersensitivity to thalidomide or Revlimid (if applicable). * The development of erythema nodosum if characterized by a desquamating rash while taking thalidomide or similar drugs. * Known seropositive for or active viral infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV). Patients who are seropositive because of hepatitis B virus vaccine are eligible. * Female subject is pregnant or lactating. Confirmation that the subject is not pregnant must be established by a negative serum -human chorionic gonadotropin (hCG) pregnancy test result obtained during screening. Pregnancy testing is not required for postmenopausal or surgically sterilized women. * Female patients who are lactating or have a positive serum pregnancy test during the screening period, or a positive urine pregnancy test on Day 1 before first dose of study drug, if applicable. * Serious medical or psychiatric illness likely to interfere with participation in this clinical study. * Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy. * Participation in clinical trials with other investigational agents not included in this trial, within 14 days of the start of this trial and throughout the duration of this trial. * Radiation therapy within 3 weeks before randomization. Enrollment of subjects who require concurrent radiotherapy (which must be localized in its field size) should be deferred until the radiotherapy is completed and 3 weeks have elapsed since the last date of therapy. * POEMS syndrome (plasma cell dyscrasia with polyneuropathy, organomegaly, endocrinopathy, monoclonal protein (M-protein) and skin changes) * Plasma cell leukemia * Receiving steroids daily for other medical conditions, e.g., asthma, systemic lupus erythematosis, rheumatoid arthritis * Infection not controlled by antibiotics * HIV infection. Patients should provide consent for HIV testing according to the institution's standard practice * Known active hepatitis B or C