Binimetinib and Palbociclib or TAS-102 in Treating Patients With KRAS and NRAS Mutant Metastatic or Unresectable Colorectal Cancer

Inclusion Criteria:

* Histological confirmation of colorectal cancer that is metastatic and/or unresectable
* Documented mutation in KRAS or NRAS (codon 12, 13, 59, 61, 117, or 146) in tumor tissue from primary or metastatic site, tested by a Clinical Laboratory Improvement Act (CLIA)-certified laboratory
* Measurable disease
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1
* Previously treated with fluoropyrimidine, oxaliplatin, and irinotecan based chemotherapy, and an anti-VEGF biological therapy
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (obtained =\< 14 days prior to registration/randomization unless otherwise noted)
* Platelet count \>= 75 x 10\^9/L without transfusions (obtained =\< 14 days prior to registration/randomization unless otherwise noted)
* Hemoglobin (Hgb) \>= 9 g/dL (obtained =\< 14 days prior to registration/randomization unless otherwise noted)
* Total bilirubin =\< 1.5 x upper limit of normal (ULN) (obtained =\< 14 days prior to registration/randomization unless otherwise noted)
* Aspartate transaminase (AST) and alanine aminotransferase (ALT) =\< 2.5 x ULN; =\< 5.0 x ULN if known liver metastases (obtained =\< 14 days prior to registration/randomization unless otherwise noted)
* Serum creatinine =\< 1.5 mg/dL OR calculated creatinine clearance \>= 50 mL/min using the Cockcroft-Gault formula (obtained =\< 14 days prior to registration/randomization unless otherwise noted)
* Negative serum beta-human chorionic gonadotropin (B-HCG) pregnancy test done =\< 7 days prior to registration/randomization for women of childbearing potential only
* Able to swallow capsules with no surgical or anatomic conditions that would preclude the patient from swallowing and absorbing oral medications
* Able and willing to provide informed written consent and able to comply with protocol requirement
* Able and willing to return to enrolling institution for follow-up (during the active monitoring phase of the study)

  * NOTE: During the active monitoring phase of a study (i.e., active treatment and observation), participants must be willing to return to the consenting institution for follow-up
* Willing to provide blood and tissue samples for mandatory correlative research purposes
* Patient is deemed by the investigator to have the initiative and means to be compliant with the protocol (treatment and follow-up)
* CROSSOVER INCLUSION CRITERIA: Histological confirmation of colorectal cancer that is metastatic and/or unresectable
* CROSSOVER INCLUSION CRITERIA: Documented mutation in KRAS or NRAS (codon 12, 13, 59, 61, 117, or 146) in tumor tissue from primary or metastatic site, tested by a CLIA-certified laboratory
* CROSSOVER INCLUSION CRITERIA: Measurable disease
* CROSSOVER INCLUSION CRITERIA: ECOG performance status (PS) of 0 or 1
* CROSSOVER INCLUSION CRITERIA: Previously treated with fluoropyrimidine, oxaliplatin, and irinotecan based chemotherapy, and an anti-VEGF biological therapy
* CROSSOVER INCLUSION CRITERIA: ANC \>= 1.5 x 10\^9/L (obtained =\< 28 days of re-registration unless otherwise noted)
* CROSSOVER INCLUSION CRITERIA: Platelet count \>= 75 x 10\^9/L without transfusion (obtained =\< 28 days of re-registration unless otherwise noted)
* CROSSOVER INCLUSION CRITERIA: Hgb \>= 9 g/dL (obtained =\< 28 days of re-registration unless otherwise noted)
* CROSSOVER INCLUSION CRITERIA: Total bilirubin =\< 1.5 x ULN (obtained =\< 28 days of re-registration unless otherwise noted)
* CROSSOVER INCLUSION CRITERIA: AST and ALT =\< 2.5 x ULN; =\< 5.0 x ULN if known liver metastases (obtained =\< 28 days of re-registration unless otherwise noted)
* CROSSOVER INCLUSION CRITERIA: Serum creatinine =\< 1.5 mg/dL OR calculated creatinine clearance \>= 50 mL/min using the Cockcroft-Gault formula (obtained =\< 28 days of re-registration unless otherwise noted)
* CROSSOVER INCLUSION CRITERIA: Negative serum beta-HCG pregnancy test done =\< 7 days prior to re-registration for women of childbearing potential only
* CROSSOVER INCLUSION CRITERIA: Able to swallow capsules with no surgical or anatomic conditions that would preclude the patient from swallowing and absorbing oral medications
* CROSSOVER INCLUSION CRITERIA: Able and willing to provide informed written consent and able to comply with protocol requirements
* CROSSOVER INCLUSION CRITERIA: Able and willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study)

  * NOTE: During the Active Monitoring phase of a study (i.e., active treatment and observation), participants must be willing to return to the consenting institution for follow-up
* CROSSOVER INCLUSION CRITERIA: Willing to provide blood samples for mandatory correlative research purposes
* CROSSOVER INCLUSION CRITERIA: Patient is deemed by the investigator to have the initiative and means to be compliant with the protocol (treatment and follow-up)

Exclusion Criteria:

* Prior treatment with drug targeting BRAF, MEK, ERK, or CDK family

  * NOTE: For the purpose of this protocol, prior treatment with regorafenib is allowed
* Prior treatment with trifluridine/tipiracil (TAS-102)
* Pregnant or nursing (lactating women), where pregnancy is defined as the state of a female after conception and until the termination of gestation, confirmed by a positive hCG laboratory test
* Women of child-bearing potential

  * NOTE: defined as all women physiologically capable of becoming pregnant, unless they agree to use highly effective methods of contraception throughout the study and for 8 weeks after study drug discontinuation
  * NOTE: Women are considered post-menopausal and not of child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation \>= 42 days prior to registration/randomization. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow-up hormone level assessment is she considered not of child bearing potential
* Sexually active males

  * NOTE: unless they agree to use highly effective methods of contraception throughout the study and for 12 weeks after study drug discontinuation and should not father a child in this period
* Any symptomatic brain metastasis

  * NOTE: Patients previously treated or untreated for this condition who are asymptomatic in the absence of corticosteroid and anti-epileptic therapy are allowed. Brain metastases must be stable for \>= 4 weeks prior to registration/randomization, with imaging (e.g., magnetic resonance imaging \[MRI\] or computed tomography \[CT\]) demonstrating no current evidence of progressive brain metastases at registration/randomization
* Prior treatment =\< 21 days prior to registration/randomization with any other chemotherapy, small molecule inhibitor (e.g. regorafenib), monoclonal antibody, immunotherapy, or radiotherapy

  * NOTE: All toxicities from prior therapy must be =\< grade 1 (or =\< grade 2 for peripheral neuropathy or alopecia)
* Impaired cardiovascular function or clinically significant cardiac diseases, including any of the following:

  * History of acute coronary syndromes (including myocardial infarction, unstable angina, coronary artery bypass grafting, coronary angioplasty, or stenting) \< 6 months prior to registration/randomization
  * Symptomatic chronic heart failure (i.e. grade 2 or higher), history or current evidence of clinically significant cardiac arrhythmia and/or conduction abnormality \< 6 months prior to registration/randomization except atrial fibrillation and paroxysmal supraventricular tachycardia
  * Left ventricular ejection fraction (LVEF) \< 50% as determined by a multigated acquisition (MUGA) scan or echocardiogram =\< 28 days prior to registration/randomization
* Uncontrolled hypertension, defined as persistent elevation of systolic blood pressure \>= 150 mmHg or diastolic blood pressure \>= 100mmHg despite current therapy
* History of thromboembolic or cerebrovascular events =\< 12 weeks prior registration/randomization. Examples include transient ischemic attacks, cerebrovascular accidents, hemodynamically significant (i.e. massive or submassive) deep vein thrombosis or pulmonary emboli

  * Note: Patients with either deep vein thrombosis or pulmonary emboli that does not result in hemodynamic instability are allowed to enroll as long as they are on a stable dose of anticoagulants for at least 4 weeks
  * Note: Patients with thromboembolic events related to indwelling catheters or other procedures may be enrolled
* Known history of acute or chronic pancreatitis =\< 6 months prior to registration/randomization
* Known positive serology for HIV (human immunodeficiency virus), active hepatitis B, and/or active hepatitis C infection
* Patients who have neuromuscular disorders that are associated with elevated creatine phosphokinase (CPK) (e.g. inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis, spinal muscular atrophy)
* History of chronic inflammatory bowel disease or Crohn's disease requiring medical intervention (immunomodulatory or immunosuppressive medications or surgery) =\< 12 months prior to registration/randomization
* Impaired gastrointestinal (GI) function or disease that may significantly alter the absorption of binimetinib or palbociclib (e.g., ulcerative disease, uncontrolled vomiting, malabsorption syndrome, small bowel resection with decreased intestinal absorption) in the opinion of the investigator
* History or current evidence of retinal vein occlusion (RVO) or current risk factors to RVO (e.g. uncontrolled glaucoma or ocular hypertension, history of hyperviscosity or hypercoagulability syndromes)
* Leptomeningeal disease
* Known hypersensitivity to the components of study drugs or its analogs
* Known medical, psychiatric, substance abuse, or cognitive disorder that may compromise the patient's ability to understand the patient information, give informed consent, comply with the study protocol or complete the 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 in the opinion of the investigator
* Patients who have undergone major surgery =\< 21 days prior to registration/randomization or who have not recovered from side effects of such procedures
* Any other 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 toxicity of the prescribed regimens
* Previous or concurrent malignancy =\< 3 years prior to registration/randomization with the following exceptions:

  * Adequately treated basal cell or squamous cell carcinoma of the skin
  * Superficial bladder cancer
  * Prostate intraepithelial neoplasm
  * In situ carcinoma of the cervix
  * Other solid tumors treated curatively without evidence of recurrence for \>= 3 years prior to registration/randomization

    * NOTE: If there is a history or prior malignancy, must not be receiving other specific anti-cancer treatment such as anti-estrogen, anti-androgen, or other tyrosine kinase inhibitor therapy
* CROSSOVER EXCLUSION CRITERIA: Prior treatment with drug targeting BRAF, MEK, ERK, or CDK family

  * NOTE: For the purpose of this protocol, prior treatment with regorafenib is allowed
* CROSSOVER EXCLUSION CRITERIA: Pregnant or nursing (lactating women), where pregnancy is defined as the state of a female after conception and until the termination of gestation, confirmed by a positive hCG laboratory test
* CROSSOVER EXCLUSION CRITERIA: Women of child-bearing potential

  * NOTE: Defined as all women physiologically capable of becoming pregnant, unless they agree to use highly effective methods of contraception throughout the study and for 8 weeks after study drug discontinuation
  * NOTE: Women are considered post-menopausal and not of child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation \>= 42 days of re-registration. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow-up hormone level assessment is she considered not of child bearing potential
* CROSSOVER EXCLUSION CRITERIA: Sexually active males

  * NOTE: unless they agree to use highly effective methods of contraception throughout the study and for 12 weeks after study drug discontinuation and should not father a child in this period
* CROSSOVER EXCLUSION CRITERIA: Any symptomatic brain metastasis

  * NOTE: Patients previously treated or untreated for this condition who are asymptomatic in the absence of corticosteroid and anti-epileptic therapy are allowed. Brain metastases must be stable for \>= 4 weeks, with imaging (e.g., MRI or CT) demonstrating no current evidence of progressive brain metastases at re-registration
* CROSSOVER EXCLUSION CRITERIA: Impaired cardiovascular function or clinically significant cardiac diseases, including any of the following:

  * History of acute coronary syndromes (including myocardial infarction, unstable angina, coronary artery bypass grafting, coronary angioplasty, or stenting) \< 6 months prior to re-registration
  * Symptomatic chronic heart failure (i.e., grade 2 or higher), history or current evidence of clinically significant cardiac arrhythmia and/or conduction abnormality \< 6 months prior to re-registration except atrial fibrillation and paroxysmal supraventricular tachycardia
  * Left ventricular ejection fraction (LVEF) \< 50% as determined by a MUGA scan or echocardiogram
* CROSSOVER EXCLUSION CRITERIA: Uncontrolled hypertension, defined as persistent elevation of systolic blood pressure \>= 150 mmHg or diastolic blood pressure \>= 100 mmHg despite current therapy
* CROSSOVER EXCLUSION CRITERIA: History of thromboembolic or cerebrovascular events =\< 12 weeks prior re-registration. Examples include transient ischemic attacks, cerebrovascular accidents, hemodynamically significant (i.e. massive or sub-massive) deep vein thrombosis or pulmonary emboli

  * Note: Patients with either deep vein thrombosis or pulmonary emboli that does not result in hemodynamic instability are allowed to enroll as long as they are on a stable dose of anticoagulants for at least 4 weeks
  * Note: Patients with thromboembolic events relat