Inclusion Criteria:

          -  Subjects must have histologically confirmed diagnosis of multiple myeloma

          -  Subjects must have measurable disease, as defined by at least one of the following:

               -  Serum monoclonal protein M-protein level >= 0.5 g/dL

               -  Urinary M-protein excretion of >= 200 mg over a 24-hour period

               -  Involved free light chain level >= 10 mg/dL, along with an abnormal free light
                  chain ratio

          -  Subjects must have disease that has relapsed and/or refractory after their most recent
             therapy, with progressive disease (PD) being defined as an increase of 25% from the
             lowest response value in any one or more of the following:

               -  Serum M-component protein (the absolute increase must be >= 0.5 g/dL) and/or

               -  Urine M-component protein (the absolute increase must be >= 200 mg/24 hours)
                  and/or

               -  Only in subjects without a measurable serum and urine M protein level: the
                  difference between involved and uninvolved free light chain (FLC) levels
                  (absolute increase) must be > 10 mg/dL

               -  Definite development of new bone lesions or soft tissue plasmacytomas or definite
                  increase in the size of existing bone lesions or soft tissue plasmacytomas

               -  Development of hypercalcemia (corrected serum calcium > 11.5 mg/dL) that can be
                  attributed solely to the plasma cell proliferative disorder

          -  Subjects with one to three lines of therapy for their disease with a prior therapy is
             defined as 2 or more cycles of therapy given as a treatment plan for multiple myeloma
             (MM) (e.g. a single-agent or combination therapy or a sequence of planned treatments
             such as induction therapy followed by autologous stem cell transplant (SCT) and then
             consolidation and/or maintenance therapy)

          -  Subjects must have achieved a partial response or better to at least one prior line of
             therapy

          -  Subjects must have an Eastern Cooperative Oncology Group (ECOG) performance status
             and/or other performance status 0, 1, or 2

          -  Absolute neutrophil count (ANC) >= 1,000/mm^3 without growth factors within 2 weeks of
             initiation of treatment

          -  Platelets >= 75,000/mm^3

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (ULN). In subjects with
             documents Gilbert's syndrome, total bilirubin =< 2 x ULN

          -  Aspartate aminotransferase (AST) serum glutamic oxaloacetic transaminase
             (SGOT)/alkaline phosphatase (ALT) serum glutamic pyruvic transaminase (SGPT) =< 3 x
             ULN

          -  Creatinine clearance >= 30 mL/min/1.73 m^2

          -  Subjects must be willing to give written consent before performance of any study
             related procedures not part of standard medical care, with the understanding that
             consent may be withdrawn by the subject at any time without prejudice to future
             medical care

          -  Female subjects who:

               -  Are postmenopausal for at least 1 year before the screening visit, OR

               -  Are surgically sterile, OR

               -  If they are of childbearing potential, agree to practice 2 effective methods of
                  contraception, at the same time, from the time of signing the informed consent
                  form through 90 days after the last dose of study drug, OR

               -  Agree to practice true abstinence when this is in line with the preferred and
                  usual lifestyle of the subject. (Periodic abstinence [e.g., calendar, ovulation,
                  symptothermal, post-ovulation methods] and withdrawal are not acceptable methods
                  of contraception)

          -  Male subjects, even if surgically sterilized (i.e., status post-vasectomy), must agree
             to one of the following:

               -  Agree to practice effective barrier contraception during the entire study
                  treatment period and through 90 days after the last dose of study drug, OR

               -  Agree to practice true abstinence when this is in line with the preferred and
                  usual lifestyle of the subject. (Periodic abstinence [e.g., calendar, ovulation,
                  symptothermal, post-ovulation methods] and withdrawal are not acceptable methods
                  of contraception)

        Exclusion Criteria:

          -  Subjects who received prior ixazomib at any time or daratumumab or other anti-CD38
             therapies, except as part of initial therapy if this was stopped to move on to SCT and
             the subject did not progress on anti-CD38 treatment

          -  Subjects are refractory to bortezomib or carfilzomib at the last exposure before this
             study (defined as subject having PD while receiving bortezomib or carfilzomib therapy
             or within 60 days after ending bortezomib or carfilzomib therapy)

          -  Subjects with known allergy to any of the study medications or their analogues

          -  Subjects planning to undergo SCT prior to PD on this study (i.e., these subjects
             should not be enrolled in order to reduce disease burden prior to transplant)

          -  Subjects receiving systemic treatment with strong cytochrome P450, family 3, subfamily
             A (CYP3A) inducers (e.g. rifampin, rifapentine, rifabutin, carbamazepine, phenytoin,
             phenobarbital) or use of St. John's wort within 14 days before randomization

          -  Subjects must have completed their most recent drug therapy directed at multiple
             myeloma in the following timeframes:

               -  Antitumor therapy (chemotherapy, antibody therapy, molecular targeted therapy,
                  retinoid therapy, hormonal therapy, or investigational agent) within 30 days of
                  study day 1

               -  Corticosteroids at least 3 weeks prior to starting therapy, except for a dose
                  equivalent to dexamethasone of =< 4 mg/day OR an emergency use of a short course
                  of corticosteroids (equivalent of dexamethasone 40 mg/day for a maximum of 4
                  days)

               -  Autologous stem cell transplantation at least 12 weeks prior to starting study
                  treatment

               -  Allogeneic stem cell transplantation at least 24 weeks prior to starting
                  treatment, and these subjects must also NOT have moderate to severe active acute
                  or chronic graft versus host disease (GVHD)

          -  Subjects with known chronic obstructive pulmonary disease (COPD) with a forced
             expiratory volume in 1 second (FEV1) < 50% of predicted normal

          -  Subjects with grade 2 or higher residual toxicities from prior therapy (including
             grade 2 or higher peripheral neuropathy or any grade neuropathy with pain) with the
             exception of alopecia

          -  Subjects who have undergone major surgery within 28 days of study day 1. NOTE:
             Subjects with planned surgical procedures to be conducted under local anesthesia may
             participate. Kyphoplasty or vertebroplasty are not considered major surgery

          -  Subjects with central nervous system involvement of myeloma

          -  Subjects with uncontrolled intercurrent illness including, but not limited to, ongoing
             or active infection requiring intravenous antibiotics or psychiatric illness/social
             situations that would limit compliance with study requirements

          -  Subjects with myocardial infarction within 6 months of study day 1, symptomatic
             congestive heart failure (New York Heart Association [NYHA] class III and higher),
             unstable angina, or uncontrolled cardiac arrhythmia (grade 2 or higher)

          -  Subjects with gastrointestinal (GI) tract disease causing the inability to take oral
             medication, malabsorption syndrome, requirement for intravenous alimentation, prior
             surgical procedures affecting absorption, uncontrolled inflammatory GI disease (e.g.,
             Crohn's disease, ulcerative colitis)

          -  Subjects with active hepatitis B or C virus infection, or known human immunodeficiency
             virus (HIV) positive

          -  Subjects diagnosed or treated for another malignancy within 2 years before study
             enrollment or previously diagnosed with another malignancy and have any evidence of
             residual disease. Subjects with nonmelanoma skin cancer or carcinoma in situ of any
             type are not excluded if they have undergone complete resection

          -  Female patients who are lactating or have a positive serum pregnancy test during the
             screening period

          -  Radiotherapy within 14 days before enrollment. If the involved field is small, 7 days
             will be considered a sufficient interval between treatment and administration of the
             ixazomib

          -  Participation in other clinical trials, including those with other investigational
             agents not included in this trial, within 30 days of the start of this trial and
             throughout the duration of this trial

          -  Patients that have previously participated in a study with ixazomib whether treated
             with ixazomib or not