Tucatinib Combined with Trastuzumab and TAS-102 for the Treatment of HER2 Positive Metastatic Colorectal Cancer in Molecularly Selected Patients, 3T Study

Inclusion Criteria:

* Registered to COLOMATE ACCRU-GI-1611 and:

  * COLOMATE Companion Trial Recommendation Form indicates patient meets molecular eligibility for enrollment to this study (at least one of the following: PIK3CA, KRAS, NRAS, or BRAF V600 mutation detected in blood from the Guardant360 assay)
  * COLOMATE Companion Trial Recommendation Form date of completion is \< 90 days prior to registration
* Age \>= 18 years
* Histologically and/or cytologically confirmed metastatic adenocarcinoma of the colon or rectum
* Life expectancy \>= 3 months in the estimation of the investigator
* Previous treatment with or contraindication to:

  * A fluoropyrimidine (e.g., 5-fluorouracil or capecitabine)
  * Oxaliplatin
  * Irinotecan
  * An anti-VEGF biological therapy (including but not limited to bevacizumab, ramucirumab, or ziv-aflibercept)
  * If the tumor has deficient mismatch repair proteins or is microsatellite instability (MSI)-High based on tumor tissue testing, an anti-PD-1 monoclonal antibody (nivolumab or pembrolizumab)
  * (Cancer Therapy List \[colorectal cancer\] is available on the Academic and Community Cancer Research United \[ACCRU\] web site)
* Radiographically measurable disease as per Response Evaulation Criteria in Solid Tumors (RECIST) version 1.1
* Molecular testing result from Clinical Laboratory Improvement Act (CLIA)-certified laboratory confirming that the tumor tissue has at least one of the following:

  * HER2 3+ by immunohistochemistry (IHC)
  * HER2 2+ by IHC and HER2 (ERBB2) amplification by in situ hybridization assay (Signal ratio \> 2.2 or gene copy number \> 6 by either fluorescence in situ hybridization (FISH) or chromogenic in situ hybridization (CISH)
  * HER2 (ERBB2) amplification by CLIA-certified next generation sequencing (NGS) assay
* Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0, 1, or 2 (Form is available on the ACCRU web site)
* Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 7 days prior to registration)
* Platelet count \>= 100,000/mm\^3 (obtained =\< 7 days prior to registration)
* Hemoglobin \> 8.0 g/dL (obtained =\< 7 days prior to registration)
* Total bilirubin =\< 1.5 x upper limit of normal (ULN) (obtained =\< 7 days prior to registration)
* Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) =\< 3 X upper limit of normal (ULN) (obtained =\< 7 days prior to registration)
* Creatinine clearance (using Cockcroft and Gault equation) \>= 50 mL/min or serum creatinine less than 1.5 x the upper limit of institutional normal (ULN) (obtained =\< 7 days prior to registration)
* International normalized ratio (INR) and activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless on medication known to alter INR and/or aPTT (obtained =\< 7 days prior to registration)
* Negative serum pregnancy test =\< 7 days prior to registration for women of childbearing potential only. Women of childbearing potential include women who have experienced menarche and who have not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or are not postmenopausal. Post menopause is defined as amenorrhea \>= 12 consecutive months Note: Women who have been amenorrheic for 12 or more months are still considered to be of childbearing potential if the amenorrhea is possibly due to prior chemotherapy, anti-estrogens, ovarian suppression or any other reversible treatment
* Sexually active subjects (men and women) agree to use medically accepted barrier methods of contraception (e.g., male or female condom) during the course of the study and for 4 months after the last dose of study drug(s), even if oral contraceptives are also used
* Willing to provide informed written consent =\< 30 days prior to registration
* Left ventricular ejection fraction (LVEF) \>= 50% as assessed by echocardiogram (ECHO) or multiple-gated acquisition scan (MUGA) documented =\< 28 days prior to registration
* 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 clinical follow-up), participants must be willing to return to the consenting institution for follow-up
* Willing to provide tissue and blood samples for correlative research purposes
* Willing to allow transfer of tissue and blood samples, clinical information, and outcome data collected from this trial for future research

Exclusion Criteria:

* Radiation therapy, hormonal therapy, biologic therapy, experimental therapy, or chemotherapy for cancer \< 21 days prior to registration
* Prior treatment with an anti-HER2 tyrosine kinase inhibitor, including but not limited to tucatinib, lapatinib, or neratinib

  * Note: Prior treatment with an anti-HER2 antibody or antibody drug conjugate is permitted (including but not limited to trastuzumab, pertuzumab, fam-trastuzumab-deruxtecan-nxki, ado-trastuzumab emtansine)
* Prior treatment with TAS-102
* Concurrent severe and/or uncontrolled medical conditions which may compromise participation in the study, including impaired heart function or clinically significant heart disease
* Not recovered to baseline or Common Terminology Criteria for Adverse Events (CTCAE) version (v)5.0 =\< Grade 1 from toxicity due to all prior therapies except alopecia, oxaliplatin-related neuropathy, and clinically insignificant electrolyte abnormalities. Congestive heart failure (CHF) must have been =\< Grade 1 in severity at the time of occurrence and must have resolved completely prior to registration
* Female patients who are pregnant or breast feeding
* Currently taking medications specified by the protocol as prohibited for administration in combination with study drug
* Known active central nervous system (CNS) metastases (patients with radiated or resected lesions are permitted, provided the lesions are fully treated and inactive, patients are asymptomatic, and no steroids have been administered \>= 30 days prior to registration)

  * Note: Steroids for treatment of other medical conditions other than CNS metastases are permitted
* Inability to swallow pills or any significant gastrointestinal disease which would preclude the adequate oral absorption of medications
* Use of a strong cytochrome P450 (CYP)2C8 inhibitor within 5 half-lives of the inhibitor or use of a strong CYP3A4 or CYP2C8 inducer within 5 days prior to registration
* Major surgical procedure, open biopsy, or significant traumatic injury =\< 28 days prior to registration (56 days for hepatectomy, open thoracotomy, major neurosurgery) or anticipation of need for major surgical procedure during the course of the study
* Serious, non-healing wound, ulcer, or bone fracture
* History of stroke (cerebrovascular accident), transient ischemic attack (TIA), myocardial infarction (MI), unstable angina, cardiac or other vascular stenting, angioplasty, or cardiac surgery =\< 6 months prior to registration
* Known history of congestive heart failure - New York Heart Association (NYHA) \>= Class II (See NYHA Classifications on the ACCRU website)
* Known history of human immunodeficiency virus (HIV) seropositivity, acute or chronic active hepatitis B or C infection, or other serious chronic infection requiring ongoing treatment
* Known chronic liver disease, autoimmune hepatitis, or sclerosing cholangitis
* Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm
* Any previously untreated or concurrent cancer that is distinct in primary site or histology from colorectal cancer except cervical cancer in-situ, treated basal cell carcinoma, or superficial bladder tumor.

  * Note: Subjects surviving a cancer that was curatively treated and without evidence of disease or biochemical relapse (undetectable prostate-specific antigen \[PSA\] for prostate cancer) for 3 or more years before registration are allowed. All cancer treatments must be completed at least 3 years prior to registration
* Unable or unwilling to abide by the study protocol or cooperate fully with the investigator or designee