Bevacizumab With or Without Anti-Endoglin Monoclonal Antibody TRC105 in Treating Patients With Recurrent Glioblastoma Multiforme

Inclusion Criteria: * Histological confirmation of grade 3 or 4 glioma, including astrocytoma, oligodendroglioma, and mixed gliomas, as determined by pre-registration central pathology review (Phase I) * Histological confirmation of glioblastoma multiforme (grade 4 astrocytoma) as determined by pre-registration central pathology review; note: gliosarcomas and other grade 4 astrocytoma variants (e.g., giant cell) are eligible; glioblastoma (GBM) with oligodendroglial features are NOT PERMITTED in this study if they are 1p19q co-deleted; sites submitting GBM with oligodendroglial features will be asked to provide results of 1p/19q co-deletion status (Phase II) * Evidence of tumor progression by MRI or computed tomography (CT) scan following radiation therapy or following the most recent anti-tumor therapy; note: patients who have had surgical treatment at recurrence are eligible if they had a resection with measurable or non-measurable residual disease on postoperative imaging or if there is imaging evidence of disease progression as compared to the first postoperative scan * Measurable or evaluable disease by gadolinium MRI or contrast CT scan; note: patients who have had a gross total resection (GTR) are eligible on the basis of evaluable disease * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * White blood cells (WBC) \>= 3,000/mL * Hemoglobin \>= 10.0 g/dL; note: this level may be reached by transfusion * Total bilirubin =\< institutional upper limit of normal (ULN) * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 2 x ULN * Creatinine =\< ULN * Life expectancy \>= 12 weeks * Negative serum pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Urine protein creatinine (UPC) ratio \< 1; note: urine protein must be screened by urine analysis for UPC ratio; for UPC ratio \>= 1.0, 24-hour urine protein must be obtained and the level should be \< 1,000 mg for registration * Fixed or decreasing dose of corticosteroids (or no corticosteroids) \>= 7 days prior to registration * Calculated glomerular filtration rate (GFR) must be \>= 60 ml/min; GFR will be calculated as needed per institutional guidelines * Any number of prior chemotherapy regimens for recurrent disease (Phase I); =\< 1 chemotherapy or other non-antiangiogenic regimen for recurrent disease (Phase II) * Last dose of bevacizumab \>= 2 weeks prior to registration (Phase I); note: for the phase II study only, prior exposure to bevacizumab is not allowed * Surgery \>= 4 weeks prior to registration * Completion of radiation therapy \>= 12 weeks prior to registration and prior chemotherapy \>= 4 weeks prior to registration (\>= 6 weeks from nitrosourea-containing regimens) * Small molecular cell cycle inhibitors \>= 2 weeks from registration * Ability to provide informed written consent * Ability to complete questionnaire(s) by themselves or with assistance * Willing to return to enrolling institution for follow-up * Willing to discontinue use of medications that inhibit platelet function \>= 10 days prior to registration; aspirin at doses greater than 325 mg/day must be discontinued \>= 10 days prior to registration and avoided through the study; note: nonsteroidal anti-inflammatory drug (NSAID) medications are recommended in place of aspirin; if NSAIDs or aspirin are used, histamine (H)-2 blockers and proton pump inhibitor (PPI) medications are recommended * Willing to provide mandatory blood and tissue samples for correlative research purposes (Phase I and II) Exclusion Criteria: * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception throughout the duration of the study and for at least 6 months after treatment has ended * Prior hypersensitivity to bevacizumab or toxicity requiring discontinuation of bevacizumab (Phase I) * Any prior exposure to any VEGF or VEGF inhibitor including, but not limited to, bevacizumab, cediranib, vandetanib, sunitinib, pazopanib, aflibercept, or sorafenib (Phase II) * Prior hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies (Phase I and II) * Prior hypersensitivity to triptan derivatives (Phase I and II) * Other active malignancy =\< 3 years prior to registration; exceptions: non-melanotic skin cancer or carcinoma-in-situ of the cervix; note: if there is a history of prior malignancy, they must not be receiving other specific treatment (other than hormonal therapy) for their cancer * Uncontrolled infection * Immunocompromised patients or patients known to be human immunodeficiency virus (HIV) positive and currently receiving combination antiretroviral therapy; patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and adverse events of the prescribed regimens * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, or psychiatric illness/social situations that would limit compliance with study requirements * History of hypertensive crisis or hypertensive encephalopathy * Clinically significant cardiovascular disease defined as follows: * Inadequately controlled hypertension (i.e., systolic blood pressure \[SBP\] \> 160 mm Hg and/or diastolic blood pressure \[DBP\] \> 90 mm Hg despite antihypertensive therapy) * History of cerebrovascular accident (CVA) within 6 months * Myocardial infarction or unstable angina within 6 months * New York Heart Association classification II, III, or IV cardiovascular disease * Serious and inadequately controlled cardiac arrhythmia * Significant vascular disease (i.e., aortic aneurysm, history of aortic dissection) * Clinically significant peripheral vascular disease * Evidence or history of bleeding diathesis (greater than normal risk of bleeding, i.e., hereditary hemorrhagic telangiectasia type I or HHT-1) or coagulopathy in the absence of therapeutic anti-coagulation or any hemorrhage/bleeding event \> grade 3 within 4 weeks prior to registration; note: patients with full-dose anticoagulants are eligible provided the patient has been on a stable dose for at least 2 weeks of low molecular weight heparin; therapeutic Coumadin and aspirin doses \> 325 mg daily are not allowed * Receiving any other investigational agent that would be considered as a treatment for the primary neoplasm * Prior treatment with TRC105 * Serious or non-healing wound, active ulcer, or untreated bone fracture * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess =\< 6 months prior to registration * History of invasive procedures defined as follows: * Major surgical procedure, open biopsy, or significant traumatic injury =\< 28 days prior to registration * Anticipation of need for major surgical procedures during the study * Core biopsy =\< 7 days prior to registration * History of significant vascular disease (i.e., aortic aneurysm requiring surgical repair, or recent peripheral arterial thrombosis) within 6 months prior to registration