‣ 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 fraction outside institutional range of normal or \< 50% (whichever is higher) as measured by echocardiogram (or multigated acquisition \[MUGA\] scan if an echocardiogram can't be performed or is inconclusive); left ventricular ejection fraction (LVEF) below lower limit of normal for site

‣ Patients should not have any of the following criteria:

⁃ With the exception of alopecia, any unresolved toxicities from prior therapy greater than Common Terminology Criteria for Adverse Events (CTCAE) grade 1 at the time of registration

• Hemoglobin \< 9 g/dL (\< 5.59 mmol/L); note: any blood transfusion must be \>= 14 days prior to the determination of a hemoglobin \>= 9 g/dL (\>= 5.59 mmol/L)

• Proteinuria 3+ on dipstick analysis or \> 500 mg/24 hours

• Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product or previous significant bowel resection that would preclude adequate absorption of capivasertib

• History of hypersensitivity to active or inactive excipients of capivasertib or drugs with a similar chemical structure or class to capivasertib

• Current disease or condition known to interfere with absorption, distribution, metabolism, or excretion of drugs

• Past medical history of interstitial lung disease, drug-induced interstitial lung disease, radiation pneumonitis which required steroid treatment, or any evidence of clinically active interstitial lung disease

• Previous allogeneic bone marrow transplant

• Known immunodeficiency syndrome

‣ Concomitant medications (only regarding NF2/CDKN2A/CDK4/CDK6/CCND1/CCND2/CCND3/CCNE1/AKT1/PIK3CA/PTEN genetic alterations):

⁃ Chronic concomitant treatment with strong inhibitors of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) inhibitors must discontinue the drug for 14 days prior to registration on the study for patients with NF2 mutation enrolled to GSK2256098, as well as for patients with AKT1/PIK3CA/PTEN mutations enrolled to capivasertib

• For NF2 patients going on to receive GSK2256098 and for patients with AKT1/PIK3CA/PTEN mutations enrolled to capivasertib: concomitant treatment with strong CYP3A4 inducers or CYP2D6 substrates is not allowed; patients must discontinue the drug 14 days prior to registration

• For NF2 patients going on to receive abemaciclib: avoid concomitant use of CYP3A inducers and strong CYP3A inhibitors; use caution with coadministered moderate or weak CYP3A inhibitors

‣ Diabetic status:

⁃ For patients with NF2 or SMO/PTCH1 mutations: No uncontrolled diabetes defined as a known diabetic with HBA1C \> 7.5 OR fasting glucose \> 140 mg/dL.

• For patients with AKT1/PIK3CA/PTEN mutations:

∙ Glycosylated hemoglobin (HbA1C) \< 8.0% (63.9 mmol/mol)

‣ No type 1 diabetes mellitus

‣ No requirement for insulin for routine diabetic management and control

‣ No requirement for more than two oral hypoglycemic medications for routine diabetic management and control

‣ Patients with a pre-existing diagnosis of type 2 diabetes mellitus must have fasting glucose \< 9.3 mmol/L (167mg/dL); fasting is defined as no caloric intake for at least 8 hours

• Patients without a pre-existing diagnosis of type 2 diabetes mellitus must have fasting glucose =\< 7.0 mmol/L (126 mg/dL); fasting is defined as no caloric intake for at least 8 hours

‣ Absolute neutrophil count (ANC) \>= 1,500/mm\^3

‣ Platelet count \>= 100,000/mm\^3

‣ Creatinine OR =\< 1.5 mg/dl x upper limit of normal (ULN) OR calculated (calc.) creatinine clearance \> 50 mL/min

‣ Urine protein:creatinine ratio (UPC) =\< 45 mg/mmol

‣ Total bilirubin =\< 1.5 x upper limit of normal (ULN); except in case of Gilbert's disease

‣ Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x ULN

‣ Sodium, potassium, total calcium (corrected for serum albumin) \& phosphorus within normal limits per institutional guidelines

‣ QTcF \< 450 msec (QT calculated using Fridericia formula)

‣ Mean resting heart rate (determined from EKG) 50-100 beats per minute (BMP) (must be obtained from 12-lead EKG defined by a triplicate EKG for patients assigned to the capivasertib arm; patients assigned to all other arms will require a single EKG

‣ No uncontrolled medical comorbidities per investigator discretion (e.g. interstitial lung disease, severe dyspnea at rest or requiring oxygen therapy, history of major surgical resection involving the stomach or small bowel, or pre-existing Crohn's disease or ulcerative colitis or a preexisting chronic condition resulting in baseline Grade 2 or higher diarrhea)

‣ ADDITIONAL REGISTRATION ELIGIBILITY CRITERIA FOR ABEMACICLIB ARM: Hemoglobin \>= 8 g/dL

‣ \* Patients may receive erythrocyte transfusions to achieve this hemoglobin level at the discretion of the investigator; initial treatment must not begin earlier than the day after the erythrocyte transfusion

‣ ADDITIONAL REGISTRATION ELIGIBILITY CRITERIA FOR ABEMACICLIB ARM: Prior Treatment

⁃ Patients who received chemotherapy must have recovered (Common Terminology Criteria for Adverse Events \[CTCAE\] grade =\< 1) from the acute effects of chemotherapy except for residual alopecia or grade 2 peripheral neuropathy prior to registration; a washout period of at least 28 days is required between last chemotherapy dose and registration (provided the patient did not receive radiotherapy)

• Patients who received adjuvant radiotherapy must have completed and fully recovered from the acute effects of radiotherapy; a washout period of at least 28 days is required between end of radiotherapy and registration

‣ ADDITIONAL REGISTRATION ELIGIBILITY CRITERIA FOR ABEMACICLIB ARM: No active bacterial infection (requiring intravenous \[IV\] antibiotics at time of initiating study treatment), fungal infection, or detectable viral infection (such as known human immunodeficiency virus positivity or with known active hepatitis B or C \[for example, hepatitis B surface antigen positive\]); screening is not required for enrollment in the absence of symptoms

‣ ADDITIONAL REGISTRATION ELIGIBILITY CRITERIA FOR ABEMACICLIB ARM: No personal history of any of the following conditions: syncope of cardiovascular etiology, ventricular arrhythmia of pathological origin (including, but not limited to, ventricular tachycardia and ventricular fibrillation), or sudden cardiac arrest