This study is testing a combination of chemo-immuno therapy called RBM. RBM consists of combination of drugs: rituximab, bendamustine, and melphalan followed by reinfusion of the participants own stem cells which is called autologous stem cell transplant (ASCT). Compared to the standard BEAM regimen, this RBM regimen may or may not be less effective in lymphoma, but will likely have fewer side effects.

Inclusion Criteria:

Phase I eligibility:

• Any patient with multiple myeloma B-cell non-Hodgkin lymphoma would be eligible for phase I portion of the study.

Dose expansion eligibility:

• Histologically confirmed diagnosis of multiple myeloma or rel/ref DLBCL, or diffuse large B cell lymphoma transformed from an indolent lymphoma Since the endpoint of the Phase I portion is safety, any patient with myeloma or B-cell NHL can be enrolled. For dose expansion study patients with myeloma and B-NHL will be analyzed separately. The PFS endpoint varies greatly amongst different types of lymphoma. In order to accurately interpret the survival data as secondary endpoint, a homogeneous cohort of patients with DLBCL will be evaluated. DLBCL is the most aggressive B-NHL with limited options. Other B-NHL's are generally more indolent and have more options available to them.

Additional eligibility for both the phase I and dose expansion cohort:

• Patients between the ages of 65 to 69 years old with a Hematopoietic Stem Cell Transplant Comorbidity Index (HCT-CI) score of 3 or higher.
• Any patient age 70 years old or older, irrespective of their Hematopoietic Stem Cell Transplant Comorbidity Index (HCT-CI) score.
• KPS ≥ 70
• Males must agree to use an acceptable form of contraception per institutional practices.
• Complete or partial response to salvage chemotherapy by IWG Working Group Criteria
• Cardiac ejection fraction of ≥ 45%
• Hemoglobin-adjusted diffusing capacity of carbon monoxide (DLCO) of ≥45%
• Creatinine clearance of ≥50 mL/min
• Completion of most recent salvage therapy within 8 weeks of enrollment
• Direct bilirubin ≤2.0 mg/dL in the absence of suspected Gilbert's disease (if Gilbert's disease is suspected, the total bilirubin must be ≤3.0 mg/dL), and AST ≤ 2.5 ULN.

Exclusion Criteria:

• In Lymphoma: Disease progression by IWG Working Group Criteria since last therapy
• Patients with history of CNS involvement
• Prior autologous (only in lymphoma) or allogeneic stem cell transplantation
• Patients who have failed bendamustine-based regimen previously
• Patients within 6 months of MI and stroke will be excluded