A Study of Melphalan With or Without Siltuximab in People With Multiple Myeloma Having an Autologous Stem Cell Transplant

Inclusion Criteria: * Histologically-confirmed symptomatic multiple myeloma undergoing autologous HCT with plan off study for melphalan 140 or 200 mg/m2 undergoing HCT within 12 months of diagnosis. * At least 60 years of age * Have at least 3 million x 10\^6 CD34+ cells/kg to be infused * KPS performance status \>60% or ECOG Performance Status score of 0-2 Within 6 weeks prior to enrollment: * Diffusion capacity \>45% (adjusted for hemoglobin) as predicted by pulmonary function testing. * LVEF \>45% by MUGA or rest ECHO * Clinical laboratory values meeting the following criteria * Platelet count ≥ 20 x 10\^9/L * ALT and AST ≤ 2.5 x ULN o Total bilirubin ≤ 2.5 x ULN; except if the elevation is due to Gilbert's syndrome * Calculated creatinine clearance \> 40 mL/min * Before enrollment, all women are expected to be not of childbearing potential as they will be age 60+. * A man who is sexually active with a woman of childbearing potential and has not had a vasectomy must agree to use a barrier method of birth control eg, either condom with spermicidal foam/gel/film/cream/suppository or partner with occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository, and all men must also not donate sperm during the study and for 3 months after receiving the last dose of study drug Exclusion Criteria: * Prior exposure to agents targeting IL-6 or the IL-6 receptor * Other malignancy within the past 2 years, except for the following if treated and not active: basal cell or nonmetastatic squamous cell carcinoma of the skin, cervical carcinoma in situ or International Federation of Gynecology and Obstetrics (FIGO) Stage 1 carcinoma of the cervix. Prostate cancer under observation may be enrolled after discussion with the MSK Principal Investigator. * Concurrent medical condition or disease (eg, autoimmune disease, active systemic Infection) that is likely to interfere with study procedures or results, or that in the opinion of the investigator would constitute a hazard for participating in the study * Ischemic heart disease requiring intervention in the prior 3 months or uncontrolled heart failure or an uncontrolled arrhythmiaQTc is \>460ms by Fridericia. If they have a right or left bundle branch block or intraventricular conduction delay then exclusion will be for \>500ms by Friderica. * Vaccination with live attenuated vaccines within 4 weeks of first study agent administration * Clinically significant infection, including known HIV or hepatitis C infection, or known hepatitis B (Hep B) surface antigen positivity. Patients with Hep B Core positivity can be enrolled if the Hep B PCR is negative, and they are on antiviral suppression. Patients with Hepatitis C Ab positive who are PCR negative and have completed Hepatitis C treatment can be enrolled. HIV with negative viral load on HAART can be enrolled. * Received an investigational drug (including investigational vaccines) or used an invasive investigational medical device within 14 days or 5 half lives before enrollment or is currently enrolled in the treatment stage of an investigational study * Had hospitalization for infection or major surgery (eg, requiring general anesthesia) within 2 weeks before enrollment or have not fully recovered from surgery. Note: subjects with surgical procedures conducted under local anesthesia may participate * A man who plans to father a child while enrolled in this study or within 3 months after the last dose of study agent.