Vismodegib, FAK Inhibitor GSK2256098, Capivasertib, and Abemaciclib in Treating Patients With Progressive Meningiomas

* Documentation of disease: * Histologic documentation: histologically proven intracranial meningioma as documented by central pathology review * Molecular documentation: Presence of SMO, PTCH1, NF2, CDKN2A, AKT1, PIK3CA, PTEN mutations, CDKN2A copy number loss, CDK4, CDK6, CCND1, CCND2, CCND3, or CCNE1 copy number gain in tumor sample as documented specifically by the central laboratory, regardless of whether prior genotype testing outside of the central laboratory was performed * Progressive OR residual disease, as defined by the following: * Residual measurable disease: residual measurable disease immediately after surgery without requirement for progression; for grade I disease, progression pre-operatively needs to be documented, with an increase in size of the measurable primary lesion on imaging by 25% or more (bidirectional area); the change must occur between scans separated by no more than 25 months; for patients with SMO/PTCH1 mutations enrolling to receive vismodegib, the change can occur between scans separated by up to 25 months; residual measurable disease will be defined by bidimensionally measurable lesions with clearly defined margins by MRI scans, with a minimum diameter of 10 mm in both dimensions * Progressive measurable disease: progression defined as an increase in size of the measurable primary lesion on imaging by 25% or more (bidirectional area); the change must occur between scans separated by no more than 25 months * Post radiation patients: patients with measurable and progressive meningioma who have received radiation are potentially eligible, but need to show evidence of progressive disease after completion of radiation; if the progressive meningioma lesion has been radiated, at least 24 weeks must have elapsed from completion of radiation to registration; if the progressive lesion is outside of the radiation field, then an interval of at least 2 weeks must have elapsed from completion of radiation to registration * Measurable disease: measurable disease is defined by a bidimensionally measurable main lesion on MRI or computed tomography (CT) images (MRI preferred) with clearly defined margins and a minimum diameter of 10 mm in both dimensions; multifocal disease is allowed * Prior treatment * Prior medical therapy is allowed but not required * No limit on number of prior therapies * No chemotherapy, or other investigational agents within 28 days prior to registration * No other concurrent investigational agents or other meningioma-directed therapy (chemotherapy, radiation) while on study; additionally, no cases of nitrosourea or mitomycin C within 6 weeks prior to registration * For patients treated with external beam radiation, interstitial brachytherapy or radiosurgery, an interval \> 4 weeks must have elapsed from completion of radiation therapy to registration; if the progressive lesion is outside of the radiation field, then an interval of at least 2 weeks must have elapsed from completion of radiation to registration * Steroid dosing stable for at least 4 days * Recovered to Common Terminology Criteria for Adverse Events (CTCAE) grade 1 or less toxicity from other agents with exception of alopecia and fatigue * No craniotomy 28 days prior to and after registration * Not pregnant and not nursing: \* A female of childbearing potential is a sexually mature female who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) 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) * For patients with NF2/CDKN2A/AKT1/PIK3CA/PTEN mutation, CKDN2A copy number loss, or CDK4/CDK6/CCND1/CCND2/CCND3/CCNE1 copy number gain: Age \>= 18 years * For patients with SMO/PTCH1 mutation: Age \>= 30 years * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Patient history: * Patients with history of neurofibromatosis (NF) may have other stable central nervous system (CNS) tumors (schwannoma, acoustic neuroma or ependymoma) if lesions have been stable for 6 months * No metastatic meningiomas (as defined by extracranial meningiomas outside of CNS) allowed; spinal meningiomas are allowed * No history of allergic reactions attributed to compounds of similar or biologic composition to assigned study drug * No known active hepatitis B or C * No current Child Pugh class B or C liver disease * No uncontrolled gastric ulcer disease (grade 3 gastric ulcer disease within 28 days of registration) * No uncontrolled hypertension defined as blood pressure (BP) \> 140/90 * No abdominal fistula, gastrointestinal (GI) perforation, or intra-abdominal abscess within 28 days prior to registration * No major surgery within 28 days prior to registration for any patients with AKT1/PIK3CA/PTEN mutations receiving capivasertib * For patients going on to receive capivasertib (i.e. enrolled after Update #08) * Patients should not have any of the following cardiac criteria: * Any clinically important abnormalities in rhythm, conduction, or morphology of resting electrocardiogram (EKG) (e.g., complete left bundle branch block, third degree heart block) * Any factors that increase the risk of corrected QT (QTc) prolongation or risk of arrhythmic events such as heart failure, hypokalemia, potential for Torsade de Pointes, congenital long QT syndrome, family history of long QT syndrome, or unexplained sudden death under 40 years of age, or any concomitant medication known to prolong the QT interval * Experience any of the following procedures or conditions in the preceding 6 months: coronary artery bypass graft, angioplasty, vascular stent, myocardial infarction, angina pectoris, congestive heart failure New York Heart Association (NYHA) class \>= II * Uncontrolled hypertension (systolic blood pressure \[SBP\] \< 90 mmHg and/or diastolic blood pressure \[DBP\] \< 50 mmHg) * Cardiac ejection