The following criteria is provided for health care professionals.

Inclusion Criteria:

Inclusion Criteria prior to Allogeneic Hematopoietic Stem Cell Transplantation (alloHSCT):

• Willing and able to participate as a research subject and provide informed consent (Note: an LAR may sign the consent form on the partipant's behalf)
• Diagnosis of relapsed refractory multiple myeloma defined as more than 2 lines of prior therapy with at least a very good partial remission to most recent salvage therapy.
  • Patients should have R-ISS stage II or III disease at diagnosis or high risk cytogenetics by IMWG criteria (t(4;14), del(17/17p), t(14;16), t(14;20), nonhyperdiploidy, and gain(1q)) at any time since diagnosis

Note:. A line of therapy is treatment between diagnosis and progression or between two progressions

• Eligible for CD34-selected HSCT according to MSKCC adult BMT guidelines.
• Have a 10/10 matched donor
• Age ≥ 21, < 73 years.
• Karnofsky (adult) Performance Status ≥ 70%.
• Patients must have adequate organ function measured by:
  1. Cardiac: LVEF at rest must be ≥ 50%
  2.  Hepatic:
     • < 3x ULN ALT
     • < 1.5 ULN total serum bilirubin, unless there is congenital benign hyperbilirubinemia.
  3. Renal: serum creatinine <1.2 mg/dl or if serum creatinine is outside the normal range, then CrCl > 40 ml/min (measured or calculated/estimated) with dose adjustment of Fludarabine for <70ml/min
  4. Pulmonary: DLCO > 50% of predicted (corrected for hemoglobin).

Inclusion Criteria prior to Ipilimumab:

• Non progressive myeloma (partial response or better) as defined by International Myeloma Working Group (IMWG) criteria
• Engraftment of all cell lines without transfusion dependence, defined as:
  • absolute neutrophil count > 1.0K/mcL x 3 consecutive days
  • platelets > 50K/mcLx 7 consecutive days without platelet transfusion
  • no platelet or RBC transfusions within the preceding 7 days
• ≥ 80% donor chimerism in the bone marrow

Exclusion Criteria:

Exclusion Criteria prior to Allogeneic Hematopoietic Stem Cell Transplantation (alloHSCT):

• Patients ineligible for therapy with ipilimumab, for example:.

  1. Active autoimmune disease or any condition requiring systemic treatment with either corticosteroids (>10 mg daily of prednisone equivalents) or other immunosuppressive medications at enrollment. Inhaled or topical steroids and adrenal replacement doses > 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease.
  2. History of motor neuropathy considered to be of autoimmune origin (e.g., Guillain-Barre Syndrome, Myasthenia Gravis).
• Female patients who are pregnant or breast-feeding.
• Patients with plasma cell leukemia at the time of diagnosis.
• Patients who have undergone prior allogeneic hematopoietic stem cell transplantation.
• Patients who have had a previous malignancy that is not in remission.

Exclusion Criteria prior to Ipilimumab:

• Active infection or treatment for infection (patients on Cytomegalovirus (CMV) therapy will be considered eligible; patients with CMV viremia by PCR or disease with end-organ involvement will not be eligible)
• Active GVHD of any grade or prior grade 3-4 GVHD
• Active immune suppression, defined as:
  • active use of calcineurin inhibitors, mycophenolate mofetil, or other immunomodulators
  • steroid dosing exceeding 10 mg/d prednisone or equivalent
• Receiving immunomodulatory agents (ex. thalidomide, lenalidomide, pomalidomide)