Inclusion Criteria:

- Calculated creatinine clearance (using Cockcroft-Gault equation) >=20 mL/min

- Absolute neutrophil count >= 1000/mL

- Platelet count >= 75000/mL

- Hemoglobin >= 8.0 g/dL

- Patients with relapsed multiple myeloma who have already received one or more
standard treatment regimens

- 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

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

- Patients should be proteasome inhibitor naïve (including bortezomib) OR have received
less than 6 cycles of therapy with a bortezomib containing regimen and were not
refractory to the bortezomib based regimen (less than a PR or progression on or
within 60 days of discontinuation)

- Provide informed written consent

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

- Willing to return to Mayo Clinic enrolling institution for follow-up

- Recovered (ie, < Grade 1 toxicity) from the reversible effects of prior
antineoplastic therapy

Exclusion Criteria:

- Recent prior chemotherapy:

- Alkylators (e.g. melphalan, cyclophosphamide) =< 14 days prior to registration

- Anthracyclines =< 14 days prior to registration

- High dose corticosteroids, immune modulatory drugs (thalidomide or lenalidomide) =< 7
days prior to registration

- Prior therapy with any proteasome inhibitor other than bortezomib

- No concomitant high dose corticosteroids other than what is part of treatment
protocol (concurrent use of corticosteroids); EXCEPTION: Patients may be on chronic
steroids (maximum dose 20 mg/day prednisone equivalent) if they are being given for
disorders other than myeloma, i.e., adrenal insufficiency, rheumatoid arthritis, etc

- Other active malignancy =< 2 years prior to registration; EXCEPTIONS: Non-melanotic
skin cancer or carcinoma-in-situ of the cervix; NOTE: If there is a history or prior
malignancy, they must not be receiving other specific treatment for their cancer

- Any of the following:

- Pregnant women or women of reproductive ability who are unwilling to use 2 effective
methods of contraception from the time of signing the informed consent form through
30 days after the last dose of study drug

- Nursing women

- Men who are unwilling to use a condom (even if they have undergone prior vasectomy)
while having intercourse with any women, while taking the drug and for 30 days after
stopping treatment

- 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, radiotherapy, 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 2 on clinical examination during the screening period

- Major surgery within 14 days before study registration

- Systemic treatment with strong inhibitors of cytochrome P450 1A2 (CYP1A2)
(fluvoxamine, enoxacin, ciprofloxacin), strong inhibitors of cytochrome P450 3A4
(CYP3A4) (clarithromycin, telithromycin, itraconazole, voriconazole, ketoconazole,
nefazodone, posaconazole) or strong CYP3A4 inducers (rifampin, rifapentine,
rifabutin, carbamazepine, phenytoin, phenobarbital, Gingko biloba, St. John's wort)
within 14 days before the first dose of MLN9708

- Evidence of current uncontrolled cardiovascular conditions, including cardiac
arrhythmias, congestive heart failure, 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

- QTc > 470 milliseconds (msec) on a 12-lead ECG obtained during the screening period;
Note: If a machine reading is above this value, the ECG should be reviewed by a
qualified reader and confirmed on a subsequent ECG

- 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 MLN9708 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