Tivantinib in Treating Patients With Relapsed, or Relapsed and Refractory Multiple Myeloma

Inclusion Criteria: * Patients must have been previously diagnosed with histologically or cytologically confirmed symptomatic multiple myeloma, which requires the presence of all three of the following International Myeloma Working Group criteria, except as noted: * Clonal bone marrow plasma cells \>= 10% * A monoclonal protein in either serum or urine * Evidence of end-organ damage that can be attributed to the underlying plasma cell proliferative disorder (to include one of the following): * Hypercalcemia (corrected calcium \> 2.75 mmol/L or 11.5 mg/dL) * Renal insufficiency attributable to myeloma (serum creatinine \> 1.9 mg/dL) * Anemia; normochromic, normocytic with a hemoglobin value \>= 2 g/dL below the lower limit of normal, or a hemoglobin or \< 10 g/dL * Bone lytic lesions, severe osteopenia, or pathologic fractures * Patients with a biopsy-proven plasmacytoma and either a serum or urine monoclonal protein will also be considered to have met the diagnostic criteria for multiple myeloma in the absence of clonal marrow plasmacytosis of \>= 10% * Patients must have measurable disease, as defined by at least one of the following: * Serum monoclonal protein level \>= 0.5 g/dL for immunoglobulin (Ig)G, IgA, or IgM disease * Monoclonal protein or total serum IgD \>= 0.5 g/dL for IgD disease * 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 * Patients must have had at least one, but not more than four prior lines of therapy for their disease, with lines of therapy being separated by the presence of documented disease progression; using this definition, treatment with induction therapy, followed by high-dose chemotherapy and autologous stem cell transplantation, and finally by maintenance therapy, would constitute one line, provided that multiple myeloma did not meet criteria for progression at any time during this period * Patients with relapsed disease will be considered to be those who have had progression, as defined above, off of any therapy, and who completed their therapy more than 60 days prior to the finding of progression; patients with relapsed and refractory disease will be considered to be those who have had progression, as defined above, while still on their last line of therapy, or who progressed within 60 days of finishing their most recent therapy * Patients must have completed their most recent drug therapy directed at multiple myeloma in the following time frames: * Chemotherapy, biological therapy, immunotherapy, or an investigational therapy at least 3 weeks prior to starting c-Met inhibitor ARQ197 * Corticosteroids at least 3 weeks prior to starting ARQ 197, except for a dose equivalent to dexamethasone of no greater than 4 mg/day * Nitrosoureas, nitrogen mustards, mitomycin C, or monoclonal antibodies at least 6 weeks prior to starting ARQ 197 * Autologous stem cell transplantation at least 12 weeks prior to starting ARQ 197 * Allogeneic stem cell transplantation at least 24 weeks prior to starting ARQ 197, and these patients must also not have moderate to severe active acute or chronic graft-versus-host disease * Patients must be willing and able to provide voluntary written informed consent, with the understanding that consent may be withdrawn by the subject at any time without prejudice to their future medical care * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 (Karnofsky \>= 60%) * Absolute neutrophil count (ANC) \>= 1,000 cells/mm\^3 without growth factors within 1 week of the initiation of treatment * Total white blood cell count (WBC) \>= 2,000 cells/mm\^3 without growth factors within 1 week of the initiation of treatment * Hemoglobin \>= 8 g/dL without red blood cell transfusions within 2 weeks of the initiation of treatment * Platelet counts of \>= 100,000 cells/mm\^3 for patients who have bone marrow plasmacytosis of \< 50%, or \>= 50,000 cells/mm\^3 for patients who have bone marrow plasmacytosis of \>= 50% * Total bilirubin =\< 1.5 times the upper limit of the institutional normal (ULN) values * Total aspartate aminotransferase (AST) (serum glutamic oxaloacetic acid transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 times ULN values * Serum creatinine within the institutional normal limits OR if the creatinine is elevated, creatinine clearance (CrCl) \>= 30 mL/min., as measured by a 24-hour urine collection, or estimated by the Cockcroft and Gault formula * Patients must have evidence of adequate cardiac function, as defined by the following: * Absence of New York Heart Association (NYHA) class II, III, or IV congestive heart failure * Absence of uncontrolled angina or hypertension * Absence of myocardial infarction in the previous 6 months * Absence of clinically significant bradycardia or other uncontrolled cardiac arrhythmia defined as grade 3 or 4 according to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), version 4.0 * Patients who have received radiation therapy must have completed this at least 4 weeks prior to starting therapy with ARQ 197, with the following exceptions: * Local radiation therapy to enhance bone healing of a pathologic fracture may have been performed, as long as it was completed at least 2 weeks prior to starting ARQ 197 * Local radiation therapy to treat post-fracture pain that is refractory to analgesics may have been performed, as long as it was completed at least 2 weeks prior to starting ARQ197 * Patients who have undergone any recent major surgery must have done so at least 4 weeks prior to starting therapy with ARQ 197, with the following exceptions: * Vertebroplasty and/or kyphoplasty, which must have been performed at least 1 week prior to starting ARQ 197 * Planned elective surgery unrelated to the patient's diagnosis of multiple myeloma, such as hernia repair, may be allowed, at the discretion of the Principal Investigator, as long as it was performed at least 2 weeks prior to starting ARQ 197, and patients have recovered fully from this procedure * Human immunodeficiency virus (HIV)-seropositive patients with acceptable organ function who meet the patient selection criteria, and who are not on combination antiretroviral therapy, and whose absolute CD4+ count is \>= 400 cells per cubic millimeter of blood, will be eligible; however, HIV positive patients on combination antiretroviral therapy will be ineligible * Male patients must agree to use an adequate method of contraception for the duration of the study since the effects of ARQ 197 on the developing human fetus are unknown; female patients must be either post- menopausal, free from menses for \>= 2 years, surgically sterilized, or willing to use two adequate barrier methods of contraception to prevent pregnancy, or must agree to abstain from heterosexual activity throughout the study; female patients of childbearing potential must have a negative serum (beta-human chorionic gonadotropin \[beta-HCG\]) or urine pregnancy test before receiving the first dose of ARQ 197; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately Exclusion Criteria: * Patients who are receiving any concurrent investigational agent with known or suspected activity against multiple myeloma, or those whose adverse events due to agents administered more than 4 weeks earlier have not recovered to a severity of grade 0 or grade 1 * Patients who have known central nervous system involvement with multiple myeloma will be excluded from this clinical trial * Patients who have previously been treated with another agent targeting the HGF/c-Met axis, including either monoclonal antibodies to HGF or c-Met, or small molecule inhibitors of c-Met * Patients with a known history of allergic reactions attributed to compounds of similar chemical or biologic composition to ARQ 197 * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements, in the opinion of the Principal Investigator * Pregnant or lactating women are excluded from this study * HIV positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with ARQ 197; however, HIV seropositive patients with acceptable organ function who meet the patient selection criteria, and who are not on combination antiretroviral therapy, will be eligible * Patients with non-secretory multiple myeloma, active plasma cell leukemia, defined as either having 20% of peripheral white blood cells comprised of CD138+ plasma cells, or an absolute plasma cell count of 2 x 10\^9/L, known amyloidosis, or known POEMS syndrome (plasma cell dyscrasia with polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes) * Patients who have required plasmapheresis and exchange less than 2 weeks prior to initiation of therapy with ARQ 197 * Patients with known active hepatitis A, B, and/or C infection * Patients with a "currently active" second malignancy, other than non-melanoma skin cancer and carcinoma in situ of the cervix, should not be enrolled; patients are not considered to have a "currently active" malignancy if they have completed therapy for a prior malignancy, are disease free from prior malignancies for \> 5 years, and are considered by their physician to be at less than 30% risk of relapse; in addition, patients with basal cell carcinoma of the skin, superficial carcinoma of the bladder, carcinoma of the prostate with a current prostate-specific antigen (PSA) value of \< 0.5 ng/mL, or cervical intraepithelial neoplasia will be eligible; finally, patients who are on hormonal therapy for a history of either prostate cancer or breast cancer may enroll, provided that there has been no evidence of disease progression during the previous three years