• 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