Inclusion Criteria:

• * PHASE IB AND II: Patients over age of 18
• * PHASE IB AND II: Available archival tissue for confirmatory central HER2 testing. Results not required prior to enrollment.
• * PHASE IB AND II: Left ventricular ejection fraction (LVEF) \>= 50% based on echocardiogram or multigated acquisition (MUGA).
• * PHASE IB AND II: Platelet count \>= 100,000/mm\^3 (within 7 days before enrollment)
• * For Phase Ib only: Phase Ib allows for red blood cell transfusion, filgrastim (G-CSF), and hydration to meet eligibility requirements at the discretion of the investigator
• * PHASE IB AND II: Hemoglobin \>= 9.0 g/dL (within 7 days before enrollment)
• * For Phase Ib only: Phase Ib allows for red blood cell transfusion, G-CSF, and hydration to meet eligibility requirements at the discretion of the investigator
• * PHASE IB AND II: Absolute neutrophil count (ANC) \>= 1500/mm\^3 (within 7 days before enrollment)
• * For Phase Ib only: Phase Ib allows for red blood cell transfusion, G-CSF, and hydration to meet eligibility requirements at the discretion of the investigator
• * PHASE IB AND II: Creatinine clearance \>= 30 mL/min as calculated using the Cockcroft-Gault equation or Serum creatinine =\< 1.5 × upper limit of normal (ULN) (within 7 days before enrollment)
• * For Phase Ib only: Phase Ib allows for red blood cell transfusion, G-CSF, and hydration to meet eligibility requirements at the discretion of the investigator
• * PHASE IB AND II: Alanine aminotransferase (ALT) \< 2.5 × ULN, except for patients with liver metastasis, who are only included if the ALT is \< 5 × ULN (within 7 days before enrollment)
• * PHASE IB AND II: Aspartate aminotransferase (AST) \< 2.5 × ULN, except for patients with liver metastasis, who are only included if the AST is \< 5 × ULN (within 7 days before enrollment)
• * PHASE IB AND II: Total bilirubin =\< 1.5 x ULN. Participants with Gilbert's syndrome with a total bilirubin =\< 2.0 times ULN and direct bilirubin within normal limits are permitted (within 7 days before enrollment)
• * PHASE IB AND II: Serum Albumin \>= 2.5 g/dL (within 7 days before enrollment)
• * PHASE IB AND II: International normalized ratio (INR)/prothrombin time (PT) and activated partial thromboplastin time (aPTT) =\< 1.5 × ULN (within 7 days before enrollment)
• * PHASE IB AND II: Potassium within normal limits or corrected to within normal limits prior to first dose
• * PHASE IB AND II: Magnesium within normal limits or corrected to within normal limits prior to first dose
• * PHASE IB AND II: Total calcium (corrected for serum albumin) within normal limits or corrected to within normal limits prior to first dose
• * PHASE IB AND II: Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures
• * PHASE IB AND II: Patient can be premenopausal, perimenopausal, or post-menopausal at the time of study entry.
• * Premenopausal status is defined as either:
• * Patient had last menstrual period within the last 12 months, OR
• * If on tamoxifen or toremifene, plasma estradiol and follicle stimulating hormone (FSH) are in the premenopausal ranges according to central/local laboratory definition, OR
• * In case of therapy-induced amenorrhea, plasma estradiol and/or FSH are in the premenopausal ranges according to central/local laboratory definition
• * Perimenopausal status is defined as neither premenopausal nor postmenopausal
• * Postmenopausal is defined as not meeting premenopausal status
• * For pre-menopausal patients: Confirmed negative serum pregnancy test (beta-hCG) before starting study treatment or patient has had a hysterectomy. Male and female participants of reproductive/childbearing potential must agree to use a highly effective form of contraception or avoid intercourse during and upon completion of the study and for at least 7 months for females and 4 months for males after the last dose of study drug
• * PHASE IB AND II: Male and female participants of reproductive/childbearing potential must agree to use a highly effective form of contraception or avoid intercourse during and upon completion of the study and for at least 7 months for females and 4 months for males after the last dose of study drug. Highly effective contraception methods include:
• * Total abstinence (when this is in line with the preferred and usual lifestyle of the patient). Periodic abstinence (e.g. calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception
• * Double barrier method of contraception. The following are considered adequate barrier methods of contraception, must use 2: diaphragm, condom (by the partner), sponge, or spermicide/spermicidal jelly.
• * Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy), total hysterectomy or tubal ligation at least 6 weeks before taking trial treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment.
• * Male partner sterilization (at least 6 months prior to randomization). For female patients on the trial the vasectomized male partner should be the sole partner for that patient. If vasectomy of the male partner is the highly effective method of contraception chosen, the success of the vasectomy should be medically confirmed according to local practice
• * Placement of an intrauterine device (IUD)
• * PHASE IB: Locally advanced/non-operable or metastatic HER2/neu amplified breast cancer, defined as 3+ by immunohistochemistry (IHC), or IHC 2+ and fluorescence in situ hybridization (FISH) + breast cancer
• * PHASE IB: Received 1 or more prior lines of HER2 directed therapy in the metastatic setting
• * PHASE IB: Recommended by the patient's treating oncologist to receive a tucatinib containing regimen as part of the next standard of care (SOC) line of therapy
• * PHASE IB: Eastern Cooperative Oncology Group (ECOG) performance status 0-2
• * PHASE IB: Measurable or non-measurable disease per RECIST 1.1
• * PHASE IB: Based on screening contrast brain magnetic resonance imaging (MRI), patients must have one of the following:
• * No evidence of brain metastases
• * Untreated brain metastases not needing immediate local therapy. For patients with untreated central nervous system (CNS) lesions \> 2.0 cm on screening contrast brain MRI, discussion with and approval from the medical monitor is required prior to enrollment
• * Previously treated brain metastases
• * Brain metastases previously treated with local therapy may either be stable since treatment or may have progressed since prior local CNS therapy, provided that there is no clinical indication for immediate re-treatment with local therapy in the opinion of the investigator
• * Patients treated with CNS local therapy for newly identified lesions found on contrast brain MRI performed during screening for this study may be eligible to enroll if all of the following criteria are met:
• * Time since whole-brain radiotherapy (WBRT) is \>= 21 days prior to first dose of treatment, time since stereotactic radiosurgery (SRS) is \>= 7 days prior to first dose of treatment, or time since surgical resection is \>= 28 days
• * Other sites of disease assessable by RECIST 1.1 are present
• * Relevant records of any CNS treatment must be available to allow for classification of target and non-target lesions
• * PHASE II: Operable HER2/neu amplified invasive breast cancer, defined as 3+ by IHC, or IHC 2+ and FISH +
• * PHASE II: Known Ki67 status
• * PHASE II: Previously untreated operable invasive carcinoma of the breast greater than 2.0 cm (cT2) in size based on imaging or physical exam or imaging. Patients with clinical node negative disease or clinical node (cN1/cN2) positive are allowed provided they are deemed to have operable disease at study entry
• * PHASE II: Patients with clinically involved lymph nodes should not have evidence of distant disease based on standard of care staging imaging prior to informed consent form (ICF) signature
• * PHASE II: Breast cancer suitable for mandatory baseline core biopsy
• * PHASE II: No prior systemic therapy or radiotherapy for currently-diagnosed invasive or non-invasive breast cancer
• * PHASE II: Eastern Cooperative Oncology Group (ECOG) performance status 0-1

Exclusion Criteria:

• * PHASE IB AND II: Concurrent therapy with any other non-protocol anti-cancer therapy
• * PHASE IB AND II: History of any other malignancy within the past 5 years, with the exception of non-melanoma skin cancer or carcinoma-in-situ of the cervix
• * PHASE IB AND II: Proteinuria estimated by urine protein: creatinine ratio \> 3.5 on a random urine sample
• * PHASE IB AND II: Uncontrolled arterial hypertension despite optimal medical management
• * PHASE IB AND II: Patient has known active hepatitis B virus (HBV) or hepatitis C virus (HCV), or Human immunodeficiency virus (HIV) infection (testing is not mandatory, unless required by local regulation)
• * PHASE IB AND II: Uncontrolled infection; active, clinically serious infections (\> Common Terminology Criteria for Adverse Events \[CTCAE\] grade 2)
• * PHASE IB AND II: Clinically significant, uncontrolled heart disease and/or cardiac repolarization abnormality, including any of the following:
• * History of documented myocardial infarction (MI), angina pectoris, symptomatic pericarditis, or coronary artery bypass graft (CABG) within 6 months prior to study entry
• * Documented cardiomyopathy
• * Left ventricular ejection fraction (LVEF) \< 50% as determined by multiple gated acquisition (MUGA) scan or echocardiogram (ECHO)
• * Long QT syndrome or family history of idiopathic sudden death or congenital long QT syndrome, or any of the following:
• * Risk factors for Torsades de Pointe (TdP) including uncorrected hypocalcemia, hypokalemia or hypomagnesemia, history of cardiac failure, or history of clinically significant/symptomatic bradycardia
• * Concomitant medication(s) with a known risk to prolong the QT interval and/or known to cause Torsades de Pointe that cannot be discontinued or replaced by safe alternative medication (e.g., within 5 half-lives or 7 days prior to starting study drug)
• * Inability to determine the corrected QT using Fridericia's formula (QTcF) interval
• * Clinically significant cardiac arrhythmias (e.g., ventricular tachycardia), complete left bundle branch block, high-grade atrioventricular (AV) block (e.g., bifascicular block, Mobitz type II and third degree AV block)
• * Systolic blood pressure (SBP) \> 160 or \< 90 mmHg
• * PHASE IB AND II: Congestive heart failure \> New York Heart Association (NYHA) class 2
• * PHASE IB AND II: History of baseline QT prolongation \> 450 msec
• * PHASE IB AND II: Unstable angina (angina symptoms at rest), new-onset angina (begun within the last 3 months)
• * PHASE IB AND II: Myocardial infarction less than 6 months before start of test drug
• * PHASE IB AND II: Anti-arrhythmic therapy (beta blockers or digoxin are permitted)
• * PHASE IB AND II: Arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism within 3 months before the start of study medication.
• * PHASE IB AND II: Participants receiving anticoagulation therapy are not allowed
• * PHASE IB AND II: Patients with evidence or history of bleeding diathesis. Any hemorrhage or bleeding event \>= CTCAE Grade 3 within 4 weeks of start of study medication
• * PHASE IB AND II: Non-healing wound or ulcer
• * PHASE IB AND II: History of, or current autoimmune disease (other than Hashimoto's thyroiditis with normal thyroid stimulating hormone \[TSH\])
• * PHASE IB AND II: Major surgical procedure or significant traumatic injury (as judged by the investigator) within 28 days before start of study medication, open biopsy within 7 days before start of study medication
• * PHASE IB AND II: Unable to swallow pills or has significant gastrointestinal disease which would preclude the adequate oral absorption of medications
• * PHASE IB AND II: Patients with seizure disorder requiring medication
• * PHASE IB AND II: Known hypersensitivity to any of the study drugs, study drug classes, or excipients in the formulation
• * PHASE IB AND II: Systemic continuous corticosteroid therapy at a daily dose higher than 15 mg prednisone or equivalent is not allowed. Patients may be using topical or inhaled corticosteroids. Previous corticosteroid therapy must be stopped or reduced to the allowed dose at least 7 days prior to the first study drug administration. If a patient is on chronic corticosteroid therapy, corticosteroids should be de-escalated to the maximum allowed dose after the patient has signed the consent document
• * PHASE IB AND II: History of having received an allogeneic bone marrow or organ transplant
• * PHASE IB AND II: Chronic oxygen therapy
• * PHASE IB AND II: 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 the first dose of study treatment
• * PHASE IB: Early stage (curable) breast cancer
• * PHASE IB: Based on screening brain MRI, patients must not have any of the following:
• * Any untreated brain lesions \> 2.0 cm in size, unless discussed with medical monitor and approval for enrollment is given
• * Ongoing use of systemic corticosteroids for control of symptoms of brain metastases at a total daily dose of \> 2 mg of dexamethasone (or equivalent). However, patients on a chronic stable dose of =\< 2 mg total daily of dexamethasone (or equivalent) may be eligible with discussion and approval by the medical monitor
• * Any brain lesion thought to require immediate local therapy, including (but not limited to) a lesion in an anatomic site where increase in size or possible treatment-related edema may pose risk to patient (e.g. brain stem lesions). Patients who undergo local treatment for such lesions identified by screening contrast brain MRI may still be eligible for the study based on criteria described under CNS inclusion criteria
• * PHASE IB: Known or suspected leptomeningeal disease (LMD) as documented by the investigator
• * PHASE IN: Have poorly controlled (\> 1/week) generalized or complex partial seizures, or manifest neurologic progression due to brain metastases notwithstanding CNS-directed therapy
• * PHASE II: Metastatic breast cancer (local spread to axillary or internal mammary lymph nodes is permitted)
• * PHASE II: Current therapy with raloxifene, tamoxifen, aromatase inhibitor, or other selective estrogen receptor modulator (SERM), gonadotrophin-releasing hormone (GNRH) agonist/antagonist, either for osteoporosis or prevention of breast cancer. Subjects must have discontinued therapies for at least 28 days prior to first baseline biopsy