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) * T…