Trastuzumab Emtansine in Treating Patients With HER2-Positive Metastatic or Locally Advanced Breast Cancer That Cannot Be Removed by Surgery

Inclusion Criteria: * Signed study-specific informed consent form * Histologically or cytologically documented breast cancer * Metastatic or unresectable locally advanced/recurrent breast cancer * HER2-positive disease documented as in situ hybridization (ISH)-positive and/or 3+ by immunohistochemistry (IHC) on previously collected tumor tissue * Absolute neutrophil count (ANC) \> 1500 cells/mm\^3 * Platelet count \> 100,000/mm\^3 * Hemoglobin \> 9.0 g/dL (patients are allowed to receive transfused red blood cells \[RBC\] to achieve this level) * Total bilirubin =\< 1.5 × upper limit of normal (ULN), except in patients with previously documented Gilbert's syndrome, in which case the direct bilirubin should be less than or equal to the ULN * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2.5 × ULN * Alkaline phosphatase =\< 2.5 × ULN (patients with hepatic and/or bone metastases: alkaline phosphatase =\< 5 × ULN) * Serum creatinine \< 1.5 × ULN * International normalized ratio (INR) \< 1.5 × ULN * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 * Left ventricular ejection fraction (LVEF) \>= 50% by either echocardiogram (ECHO) or multigated acquisition scan (MUGA) * Negative results of serum pregnancy test for premenopausal women of reproductive capacity and for women \< 12 months after entering menopause * For women of childbearing potential and men with partners of childbearing potential, agreement by the patient and/or partner to use a highly effective, non-hormonal form of contraception or two effective forms of non-hormonal contraception; female patients of childbearing potential must agree to use two effective forms of non-hormonal contraception; effective methods of contraception include: intrauterine device (IUD); female condom; male condom; diaphragm with spermicide; cervical cap; or a sterile sexual partner; male patients with partners of childbearing potential must use barrier contraception; in addition, male patients should also have their partners use another method of contraception from the time of informed consent through the duration of study activity * Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures, including thrombokinetic studies and platelet function studies Exclusion Criteria: CANCER-RELATED CRITERIA * Known platelet disorder, such as von Willebrand's disease or baseline platelet count of \< 100,000/mm\^3 * Chemotherapy =\< 21 days before first study treatment * Trastuzumab =\< 21 days before first study treatment * Lapatinib =\< 14 days before first study treatment * Investigational therapy or any other therapy =\< 28 days before first study treatment * Any prior ado-trastuzumab emtansine * Previous radiotherapy for the treatment of unresectable, locally advanced/recurrent or metastatic breast cancer is not allowed if: * The last fraction of radiotherapy has been administered within 14 days of first on-study thormbokinetic study * The patient has not recovered from any resulting acute toxicity (to grade =\< 1) prior to first on-study thormbokinetic study * Brain metastases that are untreated or symptomatic, or require any radiation, surgery, or steroid therapy to control symptoms from brain metastases within 14 days of first on-study thrombokinetic study; for patients with newly diagnosed brain metastases or unequivocal progression of brain metastases on screening scans, localized treatment (i.e., surgery, radiosurgery, and/or whole brain radiotherapy) is required before study enrollment; subjects with known brain metastases must have clinically controlled neurologic symptoms, defined as surgical excision and/or radiation therapy followed by 14 days of stable neurologic function prior to the first thrombokinetic procedure; patients with small brain metastases not symptomatic and deemed requiring treatment by managing clinicians or study investigators may be permitted to enroll on study * History of intolerance (including grade 3 or 4 infusion reaction) or hypersensitivity to trastuzumab or murine proteins * Current peripheral neuropathy of grade \>= 3 per the National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) v. 4.0 * Current use of any platelet functioning inhibitors (including aspirin) within 14 days of first on-study thrombokinetic study CARDIOPULMONARY FUNCTION CRITERIA * Current unstable ventricular arrhythmia requiring treatment * History of symptomatic congestive heart failure (CHF) (New York Heart Association \[NYHA\] classes II-IV) * History of myocardial infarction or unstable angina within 6 months of enrollment * History of a decrease in LVEF to \< 40% or symptomatic CHF with previous trastuzumab treatment * Severe dyspnea at rest due to complications of advanced malignancy or requiring current continuous oxygen therapy GENERAL CRITERIA * Current severe, uncontrolled non-cancer systemic disease (e.g., clinically significant cardiovascular, pulmonary, or metabolic disease) resulting in a life expectancy of \< 6 months * Major surgical procedure or significant traumatic injury within 28 days before enrollment or anticipation of the need for major surgery during the course of study treatment * Current pregnancy or lactation * Current known active infection with human immunodeficiency virus (HIV), hepatitis B, and/or hepatitis C virus; for patients who are known carriers of hepatitis B virus (HBV), active hepatitis B infection must be ruled out based on negative serologic testing and/or determination of HBV deoxyribonucleic acid (DNA) viral load per local guidelines * Assessed by the investigator to be unable or unwilling to comply with the requirements of the protocol