Abemaciclib w/Bevacizumab in Recurrent GBM Pts w/Loss of CDKN2A/B or Gain or Amplification of CDK4/6

Inclusion Criteria: * Histologically confirmed GBM at first or second recurrence after concurrent chemoradiotherapy. Patients with an initial diagnosis of a lower-grade glioma are eligible if a subsequent biopsy was determined to be GBM. GBMs either from the initial resection or at repeat resection at recurrence must be analyzed by next-generation exome sequencing (NES) and RNA-sequencing and must have the following aberrations: * Heterozygous or homozygous loss of CDKN2A and/or CDKN2B OR * Gain or amplification of CDK4 and/or 6 NOTE: Patients with GBMs having loss of function of RB1 are EXCLUDED. * Imaging confirmation of first tumor progression or regrowth as defined by the RANO criteria. A minimum of 12 weeks must have elapsed from the completion of radiotherapy to study entry to minimize the potential for magnetic resonance imaging (MRI) changes related to radiation necrosis that might be misdiagnosed as progression of disease, unless there is a new lesion outside the radiation field or unequivocal evidence of viable tumor on histopathological sampling. * Karnofsky performance status (KPS) ≥ 60%. * Stable or decreasing dose of corticosteroids within 5 days prior to randomization. * For women who are of child-bearing potential or surgically sterile (absence of ovaries and/or uterus) and who are sexually active: to use an adequate method of contraception (oral contraceptives, intrauterine contraceptive device, barrier method of contraception in conjunction with spermicidal jelly) during the treatment period and for at least 6 months after last dose of study drug. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. For male patients who are partners of premenopausal women: agreement to use a barrier method of contraception during the treatment period and for at least 6 months after the last dose of study drug. * A female of child-bearing potential is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy; or * Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months). * Patients who have undergone recent surgery for recurrent or progressive tumor are eligible provided that: * Surgery must have confirmed the recurrence. * A minimum of 28 days must have elapsed from the day of surgery to study entry. For core or needle biopsy, a minimum of 7 days must have elapsed prior to study entry. * Craniotomy or intracranial biopsy site must be adequately healed and free of drainage or cellulitis, and the underlying cranioplasty must appear intact at the time of randomization. * Patients must be willing and able to provide written informed consent and to comply with the study protocol as judged by the investigator. * Age ≥ 18 years. * Patients must have recovered (Common Terminology Criteria for Adverse Events CTCAE\] Grade ≤1) from the acute effects of chemotherapy prior to study entry. Minimum times from prior therapies include: * ≥ 28 days elapsed from the administration of any investigational agent * ≥ 28 days elapsed from the administration of any prior cytotoxic agents, except ≥ 42 days from nitrosoureas NOTE: Prior treatment with Novo-TTF therapy is allowed at initial diagnosis, but must be discontinued prior to study entry. * Patients must be able to swallow oral medications. * Ability to understand and the willingness to sign a written informed consent. * Patients must have adequate organ and marrow function Exclusion Criteria: * Prior treatment with Bevacizumab, Abemaciclib, or any other CDK4/6 inhibitor or other systemic VEGF- or VEGF-receptor-targeted agent. * Prior treatment with prolifeprospan 20 with carmustine wafer. * Evidence of recent hemorrhage on baseline MRI of the brain. However, patients with clinically asymptomatic presence of hemosiderin, resolving hemorrhagic changes related to surgery, or presence of punctuate hemorrhage in the tumor are eligible. * Concurrent investigational agents. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to Agent(s) or other agents used in study. * 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. * Subjects must not be pregnant or nursing due to the potential for congenital abnormalities and the potential of this regimen to harm nursing infants. * Patients unable to undergo brain MRI scans with IV gadolinium. * Screening laboratory values outside of the values listed on Table 2. * Inadequately controlled hypertension (defined as systolic blood pressure \> 150 mmHg and/or diastolic blood pressure \> 100 mmHg while on antihypertensive medication). * Uncontrolled diabetes despite maximal medical management. * Prior history of hypertensive crisis or hypertensive encephalopathy. * New York Heart Association Grade II or greater congestive cardiac failure. * History of myocardial infarction (within 12 months) or unstable angina (within 6 months) prior to study entry. * History of stroke or transient ischemic attacks within 6 months prior to study entry. * Significant vascular disease (e.g. aortic aneurysm requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to study entry. * Evidence of bleeding diathesis or coagulopathy (in the absence of therapeutic anticoagulation). * History of abdominal fistula or gastrointestinal perforation within 6 months prior to study entry. * History of intracranial abscess within 6 months prior to randomization or active bacterial infection (requiring intravenous \[IV\] antibiotics within 2 weeks from initiation of study treatment), fungal infection, or detectable viral infection (such as known human immunodeficiency virus positivity or with known active hepatitis B or C \[for example, hepatitis B surface antigen positive\]. * Serious non-healing wound, active ulcer, or untreated bone fracture. * History of another malignancy in the previous 3 years, with a disease-free interval of \< 3 years. Patients with prior history of in situ cancer or basal or squamous cell skin cancer are ELIGIBLE. * Hypersensitivity to Chinese hamster ovary cell products or other recombinant human or humanized antibody. * Taking any treatments listed in the Prohibited Concomitant Medications.