Inclusion Criteria:

1. Patients must meet one of the following disease criteria:

a. Patients with high risk multiple myeloma in partial response (PR) or better with no prior progression and are ≤ 24.0 months after autologous hematopoietic cell transplantation (HCT) (single or planned tandem), or are ≤ 24.0 months after initiation of systemic anti-myeloma therapy for patients without prior autologous HCT; or

i. High risk is defined by the presence of any one of the following detected at any time prior to enrollment: deletion of chromosome 13 by conventional cytogenetics, hypodiploidy, abnormality in chromosome 1(1q amplification or 1p deletion), t(4;14), t(14;16), t(14;20) or deletion of 17p by fluorescence in situ hybridization (FISH) or conventional karyotyping; high risk criteria based on commercially available gene expression profiling (GEP)

b. Patients with high risk multiple myeloma (see criterion 2.a.i. above) in very good partial response (VGPR) or better with 1 prior progression which occurred ≤ 24.0 months after autologous HCT (single or planned tandem), or ≤ 24.0 months after initiation of systemic anti-myeloma therapy for patients without prior autologous HCT; or

i. Patients with one prior progression without measurable monoclonal paraprotein at the time of disease progression or relapse (\< 1.0 g/dl in serum or \< 200 mg/24hrs in urine) may be considered to have met VGPR criteria if \< 5% plasma cells in bone marrow and ≥ 90% decrease in the difference between involved and uninvolved free light chain (FLC) levels from baseline (time of progression/relapse).

ii. In patients with immunoglobulin G (IgG) kappa multiple myeloma (MM) receiving daratumumab: International Myeloma Working Group criteria for VGPR may not be achieved since daratumumab is known to increase the IgG kappa spike. In such cases the FLC and marrow may be used to establish VGPR, as above, with prior approval from the protocol co-chairs.

c. Patients with standard risk multiple myeloma in VGPR or better (see criteria 2.b.i. and 2.b.ii. above) at the time of enrollment with 1 prior progression ≤ 24.0 months from single or planned tandem autologous HCT; or d. Patients with primary plasma cell leukemia in VGPR or better with no prior disease progression and are ≤ 18.0 months after autologous HCT, or are ≤ 18.0 months after initiation of anti-myeloma therapy without prior autologous HCT.
2. Patients must have a related or unrelated peripheral blood stem cell donor that meet one of the following criteria:

1. A sibling donor who is a 6/6 match at HLA-A and -B (intermediate or higher resolution) and -DR Beta 1 (DRB1) (at high resolution using DNA-based typing) and must be willing to donate peripheral blood stem cells and meet institutional criteria for donation OR
2. A related donor (other than sibling) who is a 8/8 match for HLA-A, -B, -C (at intermediate or higher resolution) and -DRB1 (at high resolution using DNA-based typing) and must be willing to donate peripheral blood stem cells and meet institutional criteria for donation OR
3. An unrelated donor who is an 8/8 match at HLA-A, -B, -C, and -DRB1 (at high resolution using DNA-based typing) and must be willing to donate peripheral blood stem cells and meet institutional criteria for donation.
3. Cardiac function: Ejection fraction \> 40%
4. Estimated creatinine clearance greater than 40 mL/minute (using the Cockcroft-Gault formula and actual body weight)
5. Pulmonary function: Diffusing capacity of the lung for carbon monoxide (DLCO) ≥ 40% (adjusted for hemoglobin) and forced expiratory volume in one second (FEV1) ≥ 50%
6. Liver function: total bilirubin \< 2x the upper limit of normal and alanine aminotransferase (ALT)/aspartate aminotransferase (AST) \< 2.5x the upper normal limit (Patients with Gilbert's Disease are permitted to exceed the defined bilirubin value of 2x the upper limit of normal, however measurements of direct bilirubin should be done to confirm this diagnosis).
7. Female subjects (unless postmenopausal for at least 1 year before the screening visit, or surgically sterilized), agree to practice two (2) effective methods of contraception at the same time, or agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject (Periodic abstinence \[eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) through 90 days after the last dose of maintenance therapy (see Section 2.6.2 for definition of postmenopausal).
8. Male subjects (even if surgically sterilized) must agree to one of the following: practice effective barrier contraception (see Section 2.6.4.1 for list of barrier methods), or practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. Periodic abstinence \[eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of from the time of signing the informed consent through 90 days after last dose of maintenance therapy.
9. Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care.
10. Able to comply with the study visit schedule and other protocol requirements.

Exclusion Criteria:

1. Karnofsky Performance Score \< 70%
2. Prior allogeneic HCT
3. Patient with purely non-secretory multiple myeloma \[absence of monoclonal protein (M protein) in serum as measured by electrophoresis and immunofixation and the absence of Bence Jones protein in the urine defined by the use of conventional electrophoresis and immunofixation techniques and the absence of involved serum free light chain \> 100 mg/L\].
4. Planned pre-emptive/prophylactic administration of donor lymphocytes (as per section 2.5.2)
5. Central Nervous System (CNS) involvement with multiple myeloma defined as cerebrospinal fluid (CSF) positivity for plasma cells or a parenchymal CNS plasmacytoma
6. Patients with uncontrolled bacterial, viral or fungal infections (currently taking medication and with progression or no clinical improvement) at time of enrollment.
7. Presence of fluid collection (ascites, pleural, or pericardial effusion) that interferes with methotrexate clearance or makes methotrexate use contraindicated.
8. Patients seropositive for the human immunodeficiency virus (HIV).
9. Patient with active Hepatitis B or C determined by serology and/or nucleic acid amplification test (NAAT).
10. Patients with hypersensitivity to bortezomib, boron or mannitol.
11. Known GI disease or GI procedure that could interfere with the oral absorption or tolerance of MLN9708 (ixazomib) including difficulty swallowing.
12. Known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent.
13. Patients with ≥ grade 2 sensory peripheral neuropathy.
14. Myocardial infarction within 6 months prior to enrollment or New York Heart Association (NYHA) Class III or IV heart failure (see Appendix D), uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any ECG abnormality at screening must be documented by the investigator as not medically relevant.
15. Female patients who are lactating or pregnant
16. Prior malignancies except resected basal cell carcinoma or treated cervical carcinoma in situ. Cancer treated with curative intent ≥ 5 years previously will be allowed. Cancer treated with curative intent \< 5 years, which is in remission, will be reviewed on a case-by-case basis by the Protocol Officer or one of the Protocol Chairs.
17. Patients with multi-organ involvement by amyloidosis or evidence of amyloidosis related organ dysfunction.
18. Failure to have fully recovered (i.e., no toxicities \> Grade 1 by CTCAE version 4.0) from the reversible effects of prior chemotherapy.
19. Patient with serious medical of psychiatric illness likely to interfere with participation on this clinical study
20. Participation in clinical trials with other investigational agents not included in this trial, ≤ 14.0 days of enrollment on this trial and throughout its duration.
21. Patients who have received radiation therapy within 3 weeks before transplant. Enrollment of subjects who require concurrent radiotherapy (which must be localized in its field size) should be deferred until the radiotherapy is completed and 3 weeks have elapsed since the last date of therapy.
22. Patients unable or unwilling to adhere to the study assessment schedule.