Tivantinib and Bevacizumab in Treating Patients With Solid Tumors That Are Metastatic or Cannot Be Removed by Surgery

Inclusion Criteria:

* Patients must have histologically confirmed solid tumor malignancy (excluding squamous cell carcinoma of lung) that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective
* Patients must have measurable or evaluable disease by Response Evaluation Criteria in Solid Tumors (RECIST) (version 1.1)
* Current diagnosis of type II diabetes mellitus is eligible as long as patient glucose levels are well-controlled (fasting =\< 150 mg/dL) with anti-diabetic medication
* Patients must be able to swallow pills and no significant impairment in gastrointestinal absorption
* There are no restrictions on prior therapy:

  * Prior bevacizumab is allowed
  * Prior therapy with inhibitors of MET or HGF is allowed
* Eastern Cooperative Oncology Group (ECOG) performance status must be =\< 2 (Karnofsky \>= 60%)
* Life expectancy must be greater than 3 months
* Hemoglobin \>= 9.0 g/dL
* Leukocytes \>= 3,000/mcL
* Absolute neutrophil count \>= 1,500/mcL
* Platelets \>= 100,000/mcL
* Total bilirubin =\< 1.5 X institutional upper limit of normal (ULN)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional ULN
* Serum or plasma creatinine =\< 1.5 X institutional ULN OR creatinine clearance \>= 60 mL/min for patients with creatinine levels \> 1.5 X institutional ULN
* Urine protein =\< +1 on spot urinalysis/urine dipstick; if urine dipstick \> +1, a 24-hour urine for protein must be =\< 1 G/24 hour (hr)
* Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; 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; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of tivantinib administration
* Negative urine or serum pregnancy test within 7 days of start of protocol therapy (for female patients who have not undergone bilateral oophorectomy or hysterectomy)
* Patients must have the ability to understand and the willingness to sign a written informed consent document
* Patients must have available archival tumor tissue (formalin-fixed, paraffin-embedded) for submission of blocks or unstained slides

Exclusion Criteria:

* Patients who have had chemotherapy, monoclonal antibody therapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to start of study drugs or those who have adverse events not resolved to a grade 1 or neuropathy not resolved to =\< grade 2 due to agents administered more than 4 weeks earlier
* Major hemorrhagic or thrombotic event within 3 months of start of protocol therapy
* Major surgery within 6 weeks or non-healing wounds
* Patients who have received kinase inhibitor therapy within 2 weeks of start of protocol therapy
* Patients who are receiving any other investigational agents
* Known central nervous system (CNS) disease except for treated brain metastasis; treated brain metastases are defined as having no ongoing requirement for steroids and no evidence of progression or hemorrhage after treatment for at least 3 months, as ascertained by clinical examination and brain imaging (magnetic resonance imaging \[MRI\] or computed tomography \[CT\]); (stable dose of non-enzyme-inducing anticonvulsants are allowed); treatment for brain metastases may include whole brain radiotherapy (WBRT), radiosurgery (RS; Gamma Knife, linear accelerator \[LINAC\], or equivalent) or a combination as deemed appropriate by the treating physician; patients with CNS metastases treated by neurosurgical resection or brain biopsy performed within 3 months prior to day 1 will be excluded
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to tivantinib or bevacizumab, or to Chinese hamster ovary cells
* Tivantinib is metabolized by CYP2C19, and to a lesser extent cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4); the metabolism and consequently overall pharmacokinetics of tivantinib could be altered by inhibitors and/or inducers or other substrates of CYP2C19 and CYP3A4; while inhibitors/inducers of these cytochrome P450 isoenzymes are not specifically excluded, investigators should be aware that tivantinib exposure may be altered by the concomitant administration of these drugs; as part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, psychiatric illness/social situations that would limit compliance with study requirements
* Patients with clinically significant cardiovascular disease, including any of the following, are excluded:

  * Inadequately controlled hypertension (HTN) (systolic blood pressure \[SBP\] \> 160 mmHg and/or diastolic blood pressure \[DBP\] \> 90 mmHg despite antihypertensive medication)
  * History of cerebrovascular accident (CVA) within 6 months of start of protocol therapy
  * Myocardial infarction or unstable angina within 6 months of start of protocol therapy
  * New York Heart Association grade II or greater congestive heart failure
  * Serious and inadequately controlled cardiac arrhythmia
  * Significant vascular disease (e.g. significant aortic aneurysm, history of aortic dissection)
  * Clinically significant peripheral vascular disease
  * Untreated deep venous thrombosis (DVT) or pulmonary embolism (PE) or DVT/PE which has been treated with therapeutic anticoagulation for less than 6 weeks
* History of hemoptysis in excess of 2.5 mL (1/2 teaspoon ) within 8 weeks prior to first dose of study drug
* Pregnant women are excluded from this study, and breastfeeding should be discontinued if the mother is treated with tivantinib; these potential risks may also apply to bevacizumab
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible