Autologous Stem Cell Transplant Followed By Maintenance Therapy in Treating Elderly Patients With Multiple Myeloma

Inclusion Criteria: * Participants must have had a diagnosis of symptomatic multiple myeloma (MM), MM + amyloidosis, or POEMS (osteosclerotic myeloma: polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, skin changes) requiring treatment; participants with a previous history of smoldering myeloma will be eligible if there is evidence of progressive disease requiring chemotherapy; Note that study participants do not need to have active disease at the time of study entry, as participants may have received up to 12 months of prior chemotherapy, which might have induced a response * Protein criteria must be present at diagnosis (quantifiable M-component of IgG, IgA, IgD, or IgE and/or urinary kappa or lambda light chain, Bence-Jones protein, or Free Kappa Light Chain or Free Lambda Light Chain) in order to evaluate response. Non-secretory participants are eligible provided the participant has \> 20% plasmacytosis OR multiple (≥3) plasmacytomas or lesions on MRI at the time of diagnosis or study enrollment , OR the presence of lesions on PET/CT scan or skeletal survey at diagnosis or study enrollment. * Participants must have received ≤12 months of prior chemotherapy for this disease without evidence of progressive disease with treatment. Participants may have received prior radiotherapy provided approval has been obtained from the PI. Participants with a history of radiation who have a platelet count \<150,000 due to radiation (disease, chemo, and other factors have been ruled out) will be excluded from this study. * Participants must not have had a prior transplant * Participants must be 65-85 years of age at the time of study entry. * Ejection fraction by echocardiogram (ECHO) or multigated acquisition scan (MUGA) of \>= 40% performed * Participants must have adequate pulmonary function studies (PFTs), \>= 50% of predicted on mechanical aspects (forced expiratory volume in 1 second \[FEV\^1}, forced vital capacity \[FVC\]) and diffusion capacity (diffusion capacity of the lung for carbon monoxide \[DLCO\]) \>= 50% of predicted (adjusted for hemoglobin); if the participant is unable to complete pulmonary function tests (PFTs) due to disease-related pain or other circumstances that make it difficult to reliably perform PFTs, documentation of pulmonary function adequate for transplant will occur via a CT scan without evidence of major pulmonary disease, and arterial blood gas results * Participants must have a creatinine \< 3 mg/dl and a GFR \>30mL/min/1.73m2 * Participants must have a performance status of 0-2 based on Eastern Cooperative Oncology Group (ECOG) criteria; participants with a poor performance status (3-4) based solely on bone pain will be eligible, provided there is documentation to verify this * Participants must sign the most current institutional review board (IRB)-approved study (informed consent form) ICF Exclusion Criteria: * Prior autologous or allogeneic transplant * Progressive disease on prior treatment * Platelet count \< 30 x 10\^9/L, unless myeloma-related; if MM-related (hypercellular marrow biopsy of \> 80% and packed with at least 80% plasma cells) the enrolling investigator must document this * \> Grade 3 neuropathy * Known hypersensitivity to bortezomib, boron, or mannitol * Uncontrolled diabetes on appropriate therapy * Recent (=\< 6 months) myocardial infarction, unstable angina, difficult to control congestive heart failure, uncontrolled hypertension on appropriate therapy, or difficult-to-control cardiac arrhythmias * Participants must not have a creatinine \>3 mg/dl or a GFR \<30mL/min/1.73m2. * Participants must not have a concurrent malignancy unless it can be adequately treated by non-chemotherapeutic intervention; participants may have a history of prior malignancy, provided that he/she has not had any chemotherapy within 365 days of study entry AND that life expectancy exceeds 5 years at the time of study entry * Participants must not have life-threatening co-morbidities