Inclusion Criteria:

- Histologic diagnosis of glioblastoma (GBM), gliosarcoma, anaplastic astrocytoma (AA),
anaplastic oligodendroglioma (AO), or anaplastic mixed oligoastrocytoma (AOA).
Patients are eligible if the original histology was lower-grade glioma.

- Unequivocal progression by MRI or CT

- Patients with recurrence who undergo resection and are left without measurable or
evaluable disease are eligible.

- Patients must have recurrent disease and may have had any number of prior relapses
(including no prior relapses). Relapse is defined as progression following initial
therapy.

- 18 years of age or older

- Karnofsky performance status of 60 or greater

- Normal organ and marrow function as outlined in the protocol

- Ability to understand and the willingness to sign a written informed consent
document.

- Protocol treatment must begin within 5 consecutive days after registration

- Patients enrolled in Part 2 must be willing to undergo surgical resection and have
pre-treatment archival tumor tissue available for molecular analysis

- Women of child-bearing potential must have a negative serum or urine pregnancy test
within 72 hours before the start of the investigational product. In addition, female
subjects of child-bearing potential and male subjects with partners of child-bearing
potential must agree to use an effective means of birth control while on study
therapy and for a minimum of 1 month following last plerixafor dose.

Effective birth control includes:

- birth control pills, depot progesterone, or an intrauterine device plus one barrier
method;

- or 2 barrier methods. Effective barrier methods are male and female condoms,
diaphragms, and spermicides (creams or gels that contain a chemical to kill sperm).
Hormonal contraceptive methods are not sufficient, as information about any
interaction of plerixafor with hormonal contraceptives is not known.

Exclusion Criteria:

- Patients who have had prior chemotherapy within the past 4 weeks (6 weeks for
nitrosoureas or mitomycin C). Patients must be off treatment with Temozolomide for at
least 23 days. Patients who received non-cytotoxic drug therapy must be off treatment
for at least 2 weeks.

NOTE: Participants must have recovered to a grade 0 or 1 from the toxic effects of prior
therapy (with the exception of lymphopenia, which is common after therapy with
temozolomide).

- In order to prevent registering patients with pseudoprogression rather than true
disease progression, patients must not have received any form of cranial radiation
within 12 weeks of study entry.

NOTE: Patients who have received cranial radiation within 12 weeks of study entry will be
allowed to register to trial only if progressive disease is confirmed via biopsy.

- Major surgical procedure (including craniotomy) or significant traumatic injury less
than 28 days or those who receive minor surgical procedures (e.g. core biopsy or fine
needle aspiration) within 7 days.

- Patients may not be receiving any other investigational agents within the past 28
days.

NOTE: If agent's half-life x 5 is < 28 days, patient may have taken it within the last 28
days, provided at least 5 half-lives have passed since having last taken it.

- Patients who have had prior therapy with CXCR4 inhibitors or anti-VEGF targeted
agents. Prior therapy with thalidomide and lenalidomide is allowed.

- Patients who have received prior treatment with implanted radiotherapy or
chemotherapy sources such as wafers of polifeprosan 20 with carmustine.

- History of allergic reactions attributed to compounds of similar chemical or biologic
composition to plerixafor or bevacizumab.

- For the first 20 patients to register, no anti-coagulation is allowed; for all
subsequent patients screened, patients requiring therapeutic anticoagulation with
warfarin at baseline are excluded (however, therapeutic or prophylactic therapy with
a low-molecular weight heparin is acceptable).

- Patients must not have a known coagulopathy that increases risk of bleeding or a
history of clinically significant hemorrhages in the past.

- Patients whose MRI scan demonstrates intratumoral hemorrhage or peritumoral
hemorrhage are not eligible for treatment if deemed significant by the treating
physician.

- Patients with gastrointestinal bleeding or any other hemorrhage/bleeding event CTCAE
Grade > 3 within 30 days prior to study entry.

- 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.

- Patients with greater than 1+ proteinuria on a urine dipstick or equivalent routine
laboratory analysis will require further testing with a urine protein to creatinine
ratio.

- History of non-healing wounds or ulcers, or bone refractures within 3 months of
fracture

- HIV-positive patients on combination antiretroviral therapy

- Participants with a history of a different malignancy are ineligible except for the
following circumstances: Individuals with a history of other malignancies are
eligible if they have been disease-free for at least 3 years AND are deemed by the
investigator to be at low risk for recurrence of that malignancy. Individuals with
the following cancers are eligible if diagnosed and treated within the past 3 years:
cervical cancer in situ, and basal cell or squamous cell carcinoma of the skin.

- Pregnant and breastfeeding women

- Men or women of childbearing potential who are unwilling or unable to use an
acceptable method to avoid pregnancy for the entire study period and for up to 1
month after the last dose of study drug.