Bortezomib and Vorinostat in Treating Patients With Multiple Myeloma Who Have Undergone Autologous Stem Cell Transplant

Inclusion Criteria: * Any autologous patient who underwent high dose melphalan (\>= 140 mg/m\^2) therapy or peripheral blood stem cell (PBSC) rescue for any stage of multiple myeloma and did not participate in another clinical transplant trial whose primary endpoint is also evaluating long-term, disease-free survival, or survival * Platelet count (transfusion independent) \> 75,000 cells/mm\^3 and absolute granulocyte count \> 1500 cells/mm\^3 for 5 calendar days after recovery from high dose therapy * Consenting for study between 30 days to 120 days after transplant * Female patient of childbearing potential has a negative serum pregnancy test beta-hCG within 72 hours prior to receiving the first dose of vorinostat * Female patient is either post-menopausal, free from menses for \>= 2 years, surgically sterilized, or willing to use 2 adequate barrier methods of contraception to prevent pregnancy or agrees to abstain from heterosexual activity throughout the treatment on study, starting with visit 1 and for 3 months afterward * Male patient agrees to use an adequate method of contraception for the duration of the treatment on study and for 3 months afterward Exclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status \>= 2 * A left ventricular ejection fraction less than 45% pre-transplant * Congestive heart disease with transplant, history of myocardial infarction (MI), history of coronary artery disease, or prolonged corrected QT interval (QTC) * Total bilirubin greater than 2 mg/ml (unless history of Gilbert's disease) * Serum glutamic oxaloacetic transaminase (SGOT) or serum glutamic pyruvic transaminase (SGPT) \> 2.5 x upper limit of normal (ULN) * Creatinine clearance \< 20 ml/minute, calculated by Cockroft-Gault formula or measured urine * Cannot give informed consent * Untreated systemic infection * Poorly-controlled diabetes mellitus (DM) * \>= grade 3 peripheral neuropathy * Prior history of human immunodeficiency virus (HIV) positivity with pre-transplant evaluation or known history of hepatitis B or C * Previous history of hypersensitivity to Bortezomib, boron, or mannitol; known hypersensitivity to the components of study drug or its analogs * Require therapeutic anticoagulation treatment, especially with coumadin * Potassium (K) and magnesium (Mg) \< normal limits * Patient who has had chemotherapy, radiotherapy, or biological therapy, within 30 days (42 days for nitrosoureas or mitomycin C) prior to initial dosing with study drug(s) or who has not recovered from adverse events due to agents administered more than 30 days earlier; patients who have received localized consolidation radiation to bone only less than 30 days prior to study entry are allowed * Patient is currently participating or has participated in a study with an investigational compound or device within 30 days of initial dosing with study drugs * Patient had prior treatment with an histone deacetylase inhibitor (HDAC) inhibitor (e.g., romidespin \[depsipeptide\], NSC-630176, MS 275, LAQ-824, belinostat \[PXD-101\], LBH589, MGCD0103, CRA024781, etc.) * Patients who have received compounds with HDAC inhibitor-like activity, such as valproic acid, as anti-tumor therapy should not enroll in this study * Patients who have received such compounds for other indications, e.g. valproic acid for epilepsy, may enroll after a 30-day washout period * History of central nervous system (CNS) disease * Symptomatic ascites or pleural effusions * Patient has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Patient is, at the time of signing informed consent, a regular user (including "recreational use") of any illicit drugs, substance abuse or had a recent history (within the last year) of drug or alcohol abuse * Patient is pregnant or breast-feeding, or expecting to conceive or father children within the projected duration of the study * Patient with a history of a prior malignancy with the exception of cervical intraepithelial neoplasia; non-melanoma skin cancer; adequately treated localized prostate carcinoma with prostate-specific antigen (PSA) \< 1.0; or who has undergone potentially curative therapy with no evidence of disease for five years, and/or who is deemed at low risk for recurrence by his/her treating physician * Patient has a history or current evidence of any condition, therapy, or lab abnormality that might confound the results of the study, interfere with the patient's participation for the full duration of the study or is not in the best interest of the patient to participate * Patient has a history of a gastrointestinal surgery or other procedures that might, in the opinion of the investigator, interfere with the absorption or swallowing of the study drugs