The following criteria is provided for health care professionals.

Inclusion Criteria:

• Calculated creatinine clearance (using Cockcroft-Gault equation) >= 30 mL/min
• Absolute neutrophil count >= 1000/mL
• Untransfused platelet count >= 75000/mL
• Hemoglobin >= 8.0 g/dL
• Total bilirubin =< 1.5 x the upper limit of the normal range (ULN)
• Aspartate aminotransferase (AST) =< 3 x ULN
• 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 and carfilzomib) OR have received less than 6 cycles of therapy with a bortezomib or carfilzomib containing regimen and were not refractory to the bortezomib or carfilzomib 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 institution for follow-up during the Active Monitoring Phase of the study; Note: during the Active Monitoring Phase of a study (i.e., active treatment and observation), participants must be willing to return to the consenting institution for follow-up
• Recovered (i.e., < 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 or carfilzomib
• 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
• 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; 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 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 90 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
• Patient has >= grade 3 peripheral neuropathy, or grade 2 with pain on clinical examination during the screening period
• Major surgery within 14 days before study registration
• Systemic treatment with strong inhibitors of cytochrome P450, family 1, subfamily A, polypeptide 2 (CYP1A2) (fluvoxamine, enoxacin, ciprofloxacin), strong inhibitors of cytochrome P450, family 3, subfamily A, polypeptide 4 (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
• 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