Inclusion Criteria:

          -  PHASE I ONLY:

          -  COHORT A: multiple myeloma

          -  COHORT B: biopsy proven light chain amyloidosis with organ involvement requiring
             therapy

          -  Calculated creatinine clearance (using Cockcroft-Gault equation) >= 30 mL/min

          -  Absolute neutrophil count (ANC) >= 1000/mm^3

          -  Platelet count >= 75000/mm^3

          -  Hemoglobin >= 8.0 g/dL

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN)

          -  Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =< 3 x ULN

          -  COHORT B ONLY: alkaline phosphatase =< 750 U/L

          -  COHORT B ONLY: N-terminal pro b-type natriuretic peptide (NT-ProBNP) < 7500 ng/dL

          -  Prior therapy for the treatment of solitary plasmacytoma is permitted, but > 14 days
             should have elapsed from the last day of radiation; NOTE: prior therapy with
             clarithromycin, dehydroepiandrosterone (DHEA), anakinra, pamidronate or zoledronic
             acid is permitted; any additional agents not listed must be approved by the principal
             investigator

          -  Measurable disease of multiple myeloma as defined by at least ONE of the following:

               -  Serum monoclonal protein >= 1.0 g/dL

               -  > 200 mg of monoclonal protein in the urine on 24 hour electrophoresis

               -  Serum immunoglobulin free light chain >= 10 mg/dL AND abnormal serum
                  immunoglobulin kappa to lambda free light chain ratio

          -  COHORT B ONLY: serum immunoglobulin free light chain >= 5 mg/dL AND abnormal serum
             immunoglobulin kappa to lambda free light chain ratio

          -  Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2

          -  Previously untreated

          -  Provide informed written consent

          -  Negative pregnancy test done =< 7 days prior to registration, for women of
             childbearing potential only

          -  Willing to follow strict birth control measures as suggested by the study

               -  Female patients: if they are of childbearing potential, agree to one of the
                  following:

                    -  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, AND must also adhere to the guidelines of any
                       treatment-specific pregnancy prevention program, if applicable, 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)

               -  Male patients: even if surgically sterilized (ie, 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

                    -  Must also adhere to the guidelines of any treatment-specific pregnancy
                       prevention program, if applicable, 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)

          -  Willing to return to return to enrolling institution for follow-up (during the active
             monitoring phase of the study)

        Exclusion Criteria:

          -  Monoclonal gammopathy of undetermined significance (MGUS) or smoldering myeloma only

          -  Prior cytotoxic chemotherapy or corticosteroids for the treatment of multiple myeloma;
             NOTE: prior corticosteroid use for the treatment of non-malignant disorders is
             permitted

          -  Diagnosed or treated for another malignancy =< 2 years before study enrollment or
             previously diagnosed with another malignancy and have any evidence of residual
             disease; NOTE: patients with nonmelanoma skin cancer or carcinoma in situ of any type
             are not excluded if they have undergone complete resection

          -  Any of the following:

               -  Pregnant women

               -  Nursing women

               -  Men or women of childbearing potential who are unwilling to employ adequate
                  contraception

          -  Other co-morbidity which would interfere with patient's ability to participate in
             trial, e.g. uncontrolled infection, uncompensated heart or lung disease

          -  Other concurrent chemotherapy, or any ancillary therapy considered investigational;
             NOTE: bisphosphonates are considered to be supportive care rather than therapy, and
             are thus allowed while on protocol treatment

          -  Peripheral neuropathy >= grade 3 on clinical examination or grade 2 with pain during
             the screening period

          -  Major surgery =< 14 days prior to study registration

          -  Systemic treatment with strong CYP3A4 inducers (rifampin, rifapentine, rifabutin,
             carbamazepine, phenytoin, phenobarbital, Gingko biloba, St. John?s wort) =< 14 days
             prior to registration

          -  Evidence of current uncontrolled cardiovascular conditions (New York Heart Association
             [NYHA] class III or IV), including hypertension, cardiac arrhythmias, congestive heart
             failure, unstable angina, or myocardial infarction within the past 6 months; Note:
             prior to study entry, any electrocardiogram (ECG) abnormality at screening must be
             documented by the investigator as not medically relevant

          -  Radiotherapy =< 14 days prior to registration; NOTE: if the involved field is small, 7
             days will be considered a sufficient interval between treatment and administration of
             the ixazomib

          -  Known human immunodeficiency virus (HIV) positive

          -  Known hepatitis B surface antigen-positive status, or known or suspected active
             hepatitis C infection

          -  Any serious medical or psychiatric illness that could, in the investigator?s opinion,
             potentially interfere with the completion of treatment according to this protocol

          -  Known allergy to any of the study medications, their analogues or excipients in the
             various formulations

          -  Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral
             absorption or tolerance of ixazomib including difficulty swallowing

          -  Diarrhea > grade 1, based on the National Cancer Institute (NCI) Common Terminology
             Criteria for Adverse Events (CTCAE) grading, in the absence of antidiarrheals

          -  Participation in clinical trials with other investigational agents not included in
             this trial, =< 30 days prior to registration