Inclusion Criteria:

          -  Patients with will be eligible if they are either in partial response, or have stable
             disease after no more than two attempts of induction therapy

          -  Patients with high-risk cytogenetics, t(4:14); t(14;16), t(14:20), deletion p17, gain
             in 1q, are eligible

          -  Patients with plasma cell leukemia in >= partial remission are eligible

          -  Patients with non-quantifiable monoclonal proteins are eligible provided they meet
             other criteria for multiple myeloma and they have evaluable or measurable disease by
             other (radiographic, magnetic resonance imaging [MRI], computed tomography [CT], lytic
             measurable lesion on x-ray,) means

          -  Karnofsky performance status (KPS) >= 70%

          -  Less than 12 months since diagnosis

          -  No contraindication to the collection of a minimum of 4 x 10^6 CD34+ cells/kg by
             apheresis

          -  Bilirubin =< 1.5 mg/dl

          -  Serum glutamic-oxaloacetic transaminase (SGOT) and serum glutamate pyruvate
             transaminase (SGPT) < 2.5 x upper limits of normal

          -  Creatinine of measured or calculated creatinine clearance of >= 50 cc/min

          -  Absolute neutrophil count of > 1000/ul

          -  Platelet count of > 100,000/ul

          -  Cardiac ejection fraction >= 50% by multi-gated acquisition (MUGA) scan and/or by
             echocardiogram

          -  Forced expiratory volume in 1 second (FEV1) > 60% and diffusion capacity of the lung
             for carbon monoxide (DLCO) > 50% of predicted lower limit

          -  Women of child-bearing potential and men must agree to use adequate contraception
             (hormonal or barrier method of birth control or abstinence) prior to study entry and
             for six months following duration of study participation; should a woman become
             pregnant or suspect that she is pregnant while participating on the trial, she should
             inform her treating physician immediately; patients must be fully aware of the
             teratogenic potential of immunomodulatory drugs (ImIDs) and agree to fully comply with
             the mandated guidelines regarding contraception as stated in the informed consent and
             the patient warning document attached to the consent form; women of childbearing
             potential must have a negative pregnancy test performed within 24 hours prior to
             beginning thalidomide, except for woman who have been postmenopausal for at least 2
             years, or underwent hysterectomy; use of effective means of contraceptive should be
             started at least 2 weeks prior to initiating lenalidomide

          -  All subjects must have the ability to understand and the willingness to sign a written
             informed consent; they are to give voluntary written informed consent before
             performance of any study-related procedure not part of normal medical care, with the
             understanding that consent may be withdrawn by the subject at any time without
             prejudice to future medical care

          -  Patients should have finished their prior systemic therapy or radiation therapy, at
             least 3 weeks before cyclophosphamide or granulocyte colony-stimulating factor
             (G-CSF)/plerixafor mobilization, and should have finished dexamethasone at least 7
             days prior to Plerixafor priming; administration of bisphosphonates needs to be
             completed at least 2 weeks before cyclophosphamide priming; bisphosphonates can be
             resumed or started after day 30

        Exclusion Criteria:

          -  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

          -  Known hypersensitivity to filgrastim or to Escherichia coli (E. coli) derived proteins

          -  Inability to lie supine in a full body cast for approximately 30 minutes, the
             anticipated duration of each treatment session

          -  Previous radiation therapy to more than 20% of bone marrow containing areas, or to any
             area exceeding 2000 cGy, is an exclusion

          -  Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus
             (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core
             antibody or hepatitis B surface antigen must have a negative polymerase chain reaction
             (PCR) result before enrollment; those who are PCR positive will be excluded

          -  No other medical, or psychosocial problems, which in the opinion of the primary
             physician or principal investigator would place the patient at unacceptably high risk
             from this treatment regimen