Aurora A Kinase Inhibitor MLN8237 and Bortezomib in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion * ANC \>= 1500/uL * AST =\< 2.5 x ULN * Creatinine =\< 1.5 x ULN * Creatinine clearance as calculated by the method of Cockroft and Gault \>= 30 mL/minute * Patients with relapsed or refractory multiple myeloma requiring treatment * Patients who have received prior bortezomib therapy will be allowed on trial as long as they did not progress during bortezomib or =\< 60 days of therapy discontinuation * Negative serum pregnancy test done =\< 7 days prior to registration, for women of childbearing potential (WOCBP) only (a WOCBP is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months) * Willingness to return to enrolling institution for follow-up * Life expectancy \>= 12 weeks * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care * Female subject is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study * Male subject agrees to use an acceptable method for contraception for the duration of the study * Patients have a baseline LVEF \>= 45% at baseline * Bisphosphonates are considered to be supportive care rather than therapy, and are thus allowed while on protocol treatment * PLT \>= 100,000/uL * Total bilirubin =\<1.5 x upper limit of normal (ULN) or if total bilirubin is \> 1.5 x ULN, the direct bilirubin must be =\< 2.0 mg/dL * 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, monoclonal bone marrow plasmacytosis \>= 30% (evaluable disease), or measurable plasmacytoma * ECOG Performance Status (PS) 0, 1, or 2 * Hgb \>= 9 g/dl Exclusion * Major surgery, open biopsy (excluding bone marrow) or significant traumatic injury =\< 4 weeks prior to registration * Melphalan or other myelosuppressive agents including lenalidomide and non-myelosuppressive agents such as thalidomide or high dose corticosteroids =\< 2 weeks prior to registration * Concurrent use of corticosteroids, but 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 * Uncontrolled infection * Pregnant women or women of reproductive ability who are unwilling to use effective contraception * Nursing women * Men who are unwilling to use a condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking the drug and for 4 weeks after stopping treatment * Other co-morbidity or psychiatric illness which would interfere with patient's ability to participate in this trial * Recent history of myocardial infarction in the six months prior to registration * Uncontrolled angina or electrocardiographic evidence of acute ischemia * Severe uncontrolled ventricular arrhythmias or electrocardiographic evidence of active conduction system abnormalities * Cardiac amyloidosis with hypotension (systolic BP less than 100mmHg) * MGUS or smoldering myeloma * Serious non-healing wound, or ulcer * Known hypersensitivity to Bortezomib, boron or mannitol * Patient has \>=Grade 2 peripheral neuropathy within 14 days before enrollment * Patient has received other investigational drugs with 14 days before enrollment * Diagnosed or treated for another malignancy within 2 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy * Infection requiring systemic antibiotic therapy within 14 days preceding the first dose of study drug, or other severe infection * Inability to swallow orally administered medication * Prior allogeneic bone marrow or organ transplantation * Patients who are currently receiving digoxin, cyclosporine, tacrolimus or sirolimus * Severe cardiac comorbidity * Known positive for HIV or active infectious hepatitis, type A, B or C