Inclusion Criteria:

          -  Refractory or relapsed myeloma, defined as one or more of the following:

               -  Treated with first-line therapy including at least 2 cycles of lenalidomide,
                  bortezomib or thalidomide, and one or more of the following:

                    -  Less than partial response (PR) to first-line therapy

                    -  Relapse after first (1st) line therapy

               -  High-risk cytogenetics, defined by deletion (del)(13q) by conventional
                  cytogenetics, or by del(17p), t(4;14), t(14;16), t(14;20) or 1q+ by fluorescence
                  in situ hybridization (FISH)

               -  Relapse after a prior autologous stem cell transplant (ASCT)

               -  Plasma cell leukemia

               -  Soft tissue plasmacytoma

          -  Serum creatinine =< 1.8 mg/dL and/or estimated serum creatinine clearance >= 50 ml/min

          -  Serum glutamic oxaloacetic transaminase (SGOT) and/or serum glutamate pyruvate
             transaminase (SGPT) =< 3 x upper limit of normal

          -  Serum bilirubin =< 2 x upper limit of normal, unless proven to be due to disease
             involvement

          -  Alkaline phosphatase =< 2 x upper limit of normal, unless proven to be due to disease
             involvement

          -  Adequate pulmonary function with forced expiratory volume in 1 second (FEV1), forced
             vital capacity (FVC) and diffusion capacity of the lung for carbon monoxide (DLCO) >=
             50% of expected corrected for hemoglobin and/or volume

          -  Adequate cardiac function with left ventricular ejection fraction >= 40%

          -  No uncontrolled arrhythmias or symptomatic cardiac disease

          -  Clinically euthyroid; note: patients are permitted to receive thyroid hormone
             supplements to treat underlying hypothyroidism

          -  Zubrod performance status < 2

          -  Negative beta-human chorionic gonadotropin (HCG) test in a woman of child-bearing
             potential, defined as not post-menopausal for 12 months or no previous surgical
             sterilization

          -  Availability of >= 2.5 million cluster of differentiation (CD)34+ cells/kg previously
             apheresed

          -  Ability to provide written informed consent

        Exclusion Criteria:

          -  Prior whole brain irradiation

          -  Having received radiation therapy to head and neck (excluding eyes), and internal
             organs of chest, abdomen or pelvis in the month prior to enrollment

          -  Active hepatitis B, either active carrier (hepatitis B surface antigen positive [HBsAg
             +]) or viremic (hepatitis B virus [HBV] deoxyribonucleic acid [DNA] >= 10,000
             copies/mL, or >= 2,000 IU/mL)

          -  Evidence of either cirrhosis or stage 3-4 liver fibrosis in patients with chronic
             hepatitis C or positive hepatitis C serology

          -  Active infection requiring parenteral antibiotics

          -  Known positivity for human immunodeficiency virus (HIV)

          -  Autologous stem-cell transplant in the previous six months

          -  Needing valproic acid for any medical condition during the study or within 5 days
             prior to first panobinostat treatment

          -  Impairment of gastrointestinal (GI) function or GI disease that may significantly
             alter the absorption of panobinostat

          -  Other concurrent severe and/or uncontrolled medical conditions (e.g., uncontrolled
             diabetes or active or uncontrolled infection) including abnormal laboratory values,
             that could cause unacceptable safety risks or compromise compliance with the protocol

          -  Impaired cardiac function or clinically significant cardiac diseases, including any
             one of the following:

               -  History or presence of sustained ventricular tachyarrhythmia; (patients with a
                  history of atrial arrhythmia are eligible but should be discussed with Novartis
                  prior to enrollment)

               -  Any history of ventricular fibrillation or torsade de pointes

               -  Bradycardia defined as heart rate (HR) < 50 beats per minute (bpm); patients with
                  pacemakers are eligible if HR >= 50 bpm

               -  Screening electrocardiogram (ECG) with a corrected QT (QTc) > 470 msec

               -  Right bundle branch block + left anterior hemiblock (bifascicular block)

               -  Myocardial infarction or unstable angina =< 12 months prior to starting study
                  drug

               -  Other clinically significant heart disease (e.g., congestive heart failure [CHF]
                  New York [NY] Heart Association class III or IV , uncontrolled hypertension,
                  history of labile hypertension, or history of poor compliance with an
                  antihypertensive regimen)

          -  Have undergone major surgery =< 4 weeks prior to starting study drug or who have not
             recovered from side effects of such therapy

          -  Prior malignancy with in the last 5 years (except for basal or squamous cell
             carcinoma, or in situ cancer of the cervix)

          -  Any significant history of non-compliance to medical regimens or unwilling or unable
             to comply with the instructions given to him/her by the study staff

          -  Received targeted agents within 2 weeks or within 5 half-lives of the agent and active
             metabolites (whichever is longer) and who have not recovered from side effects of
             those therapies

          -  Having received immunotherapy or chemotherapy within 2 weeks; or radiation therapy to
             > 30% of marrow-bearing bone within =< 2 weeks prior to starting study treatment; or
             who have not yet recovered from side effects of such therapies

          -  Grade >= 3 nonhematological toxicity from prior therapy that has not resolved to =<
             grade 1