Panobinostat, Carfilzomib, and Dexamethasone in Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Diagnosis of multiple myeloma refractory to or relapsed after \>= 1 line of prior therapy (International Myeloma Working Group \[IMWG\] criteria) * Measurable disease, as indicated by one of the following: * Serum monoclonal (M)-protein \>= 1.0 g/dL * Elevated involved free light chain \>= 10 mg/dL as per IMWG criteria, and abnormal ratio * Urine Bence Jones protein \> 200 mg/24 hour (hr) * Absolute neutrophil count (ANC) \>= 750/uL * Platelet count \>= 75,000/uL * Hemoglobin \>= 7 g/dL * Creatinine =\< 2.0 mg/dL or calculated creatinine clearance \>= 30 mL/min * Total bilirubin =\< 1.5 x upper limit of normal (ULN) unless elevation is thought to be due to Gilbert's syndrome * Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamate pyruvate transaminase (SPGT) (alanine aminotransferase \[ALT\]) =\< 2.5 x ULN * Patients must avoid consumption of grapefruit, pomegranates, starfruit, Seville oranges or products containing the juice of each during the entire study and preferably 7 days before the first dose of study medications; orange juice is allowed * Women of child-bearing potential, defined as all women physiologically capable of becoming pregnant, should have a pregnancy test prior to the initiation of treatment and use highly effective methods of contraception during and for 3 months post study treatment; highly effective contraception methods include total abstinence, female sterilization, male sterilization, use of oral, injected, or implanted hormonal methods of contraception or placement of an intrauterine device (IUD) or intrauterine system (IUS) or other forms of hormonal contraception that have comparable efficacy; women using hormonal contraceptives should additionally use a barrier method of contraception; women are considered post-menopausal and not of child-bearing potential if they have had 12 months of natural amenorrhea or have had surgical bilateral oophorectomy (with or without hysterectomy), total hysterectomy, or tubal ligation at least 6 weeks ago * Sexually active males must use a condom during intercourse while taking study drug and for 6 months after stopping treatment; males should not father a child in this period; a condom is required to be used also by vasectomized men as well as during intercourse with a male partner; female partners of sexually active men should also use an effective contraception during treatment and for 6 months after their male partner has stopped taking the drug Exclusion Criteria: * Another bone marrow malignancy * Another cancer with expected survival of \< 2 years * Active viral, bacterial, or fungal infection progressing on current treatment * Clinically significant uncontrolled heart disease and/or recent cardiac event within 6 months prior to enrollment, such as: * History of angina pectoris, symptomatic pericarditis, or myocardial infarction * Left ventricular ejection fraction (LVEF) \< 45% as determined by echocardiogram (ECHO) or multi gated acquisition (MUGA) scan * History or presence of any significant, uncontrolled, or persistent cardiac arrhythmias, e.g. ventricular, supraventricular, nodal arrhythmias or conduction abnormality; stable atrial fibrillation within 6 months prior to randomization is permitted * Presence of unstable atrial fibrillation (ventricular response rate \> 100 beats per minute \[bpm\]); NOTE: patients with stable atrial fibrillation can be enrolled provided they do not meet other cardiac exclusion criteria * Resting heart rate \< 50 bpm * Complete left bundle branch block (LBBB), bifascicular block * Congenital long QT syndrome * Any clinically significant ST segment and/or T-wave abnormalities * Corrected QT (QTcF) \> 450 msec for males and \> 470 msec for females using Fridericia's correction on screening electrocardiogram (ECG) * History of documented congestive heart failure (New York Heart Association functional classification III-IV) * Uncontrolled hypertension defined by a systolic blood pressure (SBP) \>= 150 mmHg and/or diastolic blood pressure (DBP) \>= 100 mmHg with or without antihypertensive medication; NOTE: initiation or adjustment of antihypertensive medication(s) is allowed prior to screening * Other clinically significant heart disease or vascular disease * Currently taking medications that have known or definite risk of prolonging the QT interval or inducing Torsades de pointes (TdP); the medication must be discontinued or switched to a safe alternative medication prior to starting treatment; specific exception is allowed for patients on long-standing medications that have risk of prolonging QT interval or inducing TdP if screening ECG does not indicate a prolonged QT abnormality * Impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of panobinostat or dexamethasone (e.g. ulcerative disease uncontrolled nausea, vomiting, malabsorption syndrome, obstruction, or stomach and/or small bowel resection) * Unresolved diarrhea \>= Common Terminology Criteria for Adverse Events (CTCAE) grade 2 or a medical condition associated with chronic diarrhea (such as irritable bowel syndrome, inflammatory bowel disease) * Major surgery =\< 14 days prior to starting study treatment or side effects of surgery that have not recovered to \< CTCAE grade 2