Panobinostat, Gemcitabine Hydrochloride, Busulfan, and Melphalan Before Stem Cell Transplant in Treating Patients With Refractory or Relapsed Multiple Myeloma

Prior treatment

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

Other illness

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

Lab values

• 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 Secura Bio, Inc (Secura Bio) 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)

• 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