Pomalidomide in Combination With High Dose Dexamethasone and Oral Cyclophosphamide

Inclusion Criteria: * Participants must have relapsed or refractory multiple myeloma. Refractory disease is defined as patients who experience disease progression on active therapy or within 60 days after the discontinuation of therapy. Relapsed disease is defined as achievement of at least a partial response followed by disease progression after 60 days of discontinuing active therapy. * Must have measurable disease as assessed by one of the following criteria: Serum monoclonal protein ≥ 0.5 g/dL by protein electrophoresis; \>200 mg of monoclonal protein in the urine on 24 hour electrophoresis; Serum immunoglobulin free light chain ≥ 10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio * Must have received at least 2 prior therapies to include prior immunomodulatory drug (lenalidomide) and the patient must be refractory to lenalidomide (defined as progressive disease during active therapy or within 60 days of discontinuation of therapy). All previous cancer chemotherapy (bisphosphonates are not included), including surgery, must have been discontinued ≥2 weeks prior to first dose of study drug. Prior radiotherapy must have been completed \> 2 weeks prior to the start of study drug unless the radiation field would not impact marrow reserve in the opinion of the investigator. * Eastern Cooperative Oncology Group (ECOG) performance status ≤2 (Karnofsky ≥60% * Must have acceptable organ function: total bilirubin less than 1.5 mg/dL; aspartic transaminase (AST)/alanine transaminase (ALT) ≤2.5 X institutional upper limit of normal (ULN); serum creatinine \< 3mg/dL * Must have adequate hematologic function as evidenced by the following: * For the Phase I study: Absolute neutrophil count (ANC) ≥ 1000 per mm³; Platelet count ≥ 50,000 per mm³. * For the Phase II portion, patients with greater than 50% bone marrow plasmacytosis will be allowed to enter the trial if the platelet count is greater than 30,000 per mm³ and regardless of baseline absolute neutrophil count if it is felt to be related to active myeloma and if in the opinion of the investigator, growth factor support can result in improvement in the neutrophil count to greater than 1000 per mm³ (growth factor can be used during screening). * Females of childbearing potential (FCBP)† must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10 - 14 days prior to and again within 24 hours of starting pomalidomide 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 pomalidomide. FCBP must also agree to ongoing pregnancy testing. Men must agree to use a latex condom during sexual contact with a FCBP even if they have had a vasectomy. * Ability to understand and the willingness to sign a written informed consent document * Able to take aspirin (81 or 325 mg) daily as prophylactic anticoagulation (patients intolerant to acetylsalicylic acid (ASA) may use warfarin or low molecular weight heparin). * All study participants must be registered into the mandatory POMALYST REMS™ program, and be willing and able to comply with the requirements of the POMALYST REMS™ program. Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 2 weeks (see Inclusion Criteria above) or those who have not recovered from adverse events due to agents administered more than 2 weeks earlier (except for neuropathy). * Any serious medical condition, laboratory abnormality, or psychiatric illness that would prevent the patient from signing the informed consent form * Any condition, including the presence of laboratory abnormalities, which places the patient at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study. Use of any other experimental drug or therapy within 28 days of baseline. * Known hypersensitivity to thalidomide or lenalidomide * The development of erythema nodosum if characterized by a desquamating rash while taking thalidomide, pomalidomide or similar drugs * Known positive for human immunodeficiency virus (HIV) or infectious hepatitis, type A, B or C * May not be receiving any other investigational agents * Pregnant or breast feeding females (Lactating females must agree not to breast feed while taking pomalidomide). * Patients with prior pomalidomide therapy (greater than 1 cycle) are excluded. * Another active malignancy requiring treatment within the next 12 months, with the exception of basal cell skin cancer, in situ cervical cancer, in situ breast cancer and asymptomatic prostate cancer * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection (except simple urinary tract or upper respiratory tract infection), symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Inability to comply with the protocol requirements or participation in any other clinical study * Corticosteroid therapies of \>20 mg/day prednisone, \>4 mg/day dexamethasone, \>80 mg/day hydrocortisone, or equivalent * Allogeneic stem cell/bone marrow transplant within 12 months of first dose of study drug or active graft versus host disease * Patients with existing peripheral neuropathy grade \>2