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)