Doxorubicin Hydrochloride, Cyclophosphamide, and Pacltaxel With or Without Trastuzumab in Treating Women With HER2-Positive Node-Positive or High-Risk Node-Negative Breast Cancer

Inclusion Criteria: * Required tumor parameters for node positive disease: NOTE: This study will continue to use the American Joint Committee on Cancer (AJCC) 5th edition for TNM classification and staging * Operable, histologically confirmed adenocarcinoma of the female breast and positive lymph nodes * Node positivity may be determined by either an axillary node dissection or a positive sentinel node finding by hematoxylin and eosin (H\&E) * NOTE: Positive nodes refers to H\&E visible nodal metastases; immunohistochemistry (IHC) positive only cells in lymph nodes will not be considered positive nodes * One or more positive lymph nodes whose tumors are T1-3, pN1-2, M0 are eligible * cN2 disease is not eligible * pN2 disease is eligible * One positive lymph node by sentinel node biopsy or at least 6 axillary nodes must be examined on axillary node dissection with at least one positive lymph node * Metaplastic carcinoma is eligible * ER/PgR determination * HER-2 positive (pre-entry requirement for registration) * FISH must show gene amplification OR * IHC assay must show a strong positive (3+) staining score * NOTE: ductal carcinoma in situ (DCIS) components should not be counted in the determination of degree of IHC staining or FISH amplification * Required tumor parameters for high-risk node-negative disease; NOTE: This study will continue to use the AJCC 5th edition for TNM classification and staging * Operable, histologically confirmed adenocarcinoma of the female breast and negative lymph nodes * Node status may be determined by either axillary node dissection or sentinel node biopsy with H\&E staining; to be considered node negative, either of the following must be true: 1) negative sentinel node biopsy or 2) no positive lymph nodes found among at least 6 axillary nodes examined on axillary node dissection * NOTE: IHC positive only cells in lymph nodes will not be considered positive nodes * Tumors \> 2.0 cm (irrespective of hormonal receptor status) or \> 1.0 cm if ER-negative and PR-negative disease * ER/PgR determination * HER-2 positive (pre-entry requirement for registration) * FISH must show gene amplification OR * IHC assay must show a strong positive (3+) staining score * NOTE: DCIS components should not be counted in the determination of degree of IHC staining or FISH amplification * =\< 84 days from mastectomy or =\< 84 days from axillary dissection or sentinel node detection if the patient's most extensive breast surgery was a breast sparing procedure; (This timing is per a decision by the Breast Intergroup) * Surgical resection margins. All tumor should be removed by either a modified radical mastectomy or a segmental mastectomy with axillary node dissection * Mastectomy: There will be no evidence of gross or microscopic tumor (invasive or DCIS) at the surgical resection margins noted in the final surgery or pathology reports; patients with close margins are eligible * Segmental mastectomy (lumpectomy): Margins must be clear of invasive cancer and DCIS * Axillary dissection or sentinel node dissection: There will be no gross residual adenopathy * TAM therapy * May have received up to four weeks of TAM therapy, or any other hormonal agent, for this malignancy * May have received TAM or raloxifene for purposes of chemoprevention (e.g., Breast Cancer Prevention Trial) or for other indications (including previous breast cancer if lobular carcinoma in situ \[LCIS\]) but must be discontinued before registration on this study * May never have received TAM, raloxifene, or any other hormonal agent * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelets (PLT) \>= 100,000/mm\^3 * Total bilirubin =\< 1.5 x upper normal limit (UNL) * Aspartate aminotransferase (AST) =\< 2.0 x UNL * Left ventricular ejection fraction (LVEF) within institutional normal range; if LVEF is \> 75%, the investigator should consider performing a second review of the multigated acquisition (MUGA)/echocardiogram or performing a repeat MUGA/echocardiogram prior to registration; such re-reviews or repeat MUGA/echocardiogram are not permitted after registration * Willingness to discontinue sex hormonal therapy, e.g., birth control pills, ovarian hormonal replacement therapy, etc., prior to registration and while on study * Willingness to discontinue any hormonal agent such as raloxifene (Evista) prior to registration and while on study * Non-breast malignancies that have not recurred within the last 5 years and are deemed to be at low risk for recurrence EXCEPTIONS: These non-breast malignancies are eligible even if diagnosed =\< 5 years prior to registration: * Squamous or basal cell carcinoma of the skin that has been effectively treated * Carcinoma in situ of the cervix that has been treated by surgery only * Lobular carcinoma in situ (LCIS) of the ipsilateral or contralateral breast treated by surgery and/or tamoxifen only * Patients undergoing breast conservation therapy (i.e., lumpectomy and axillary dissection) must have plans to receive radiation therapy to the breast +/- regional lymphatics following completion of the chemotherapy; for patients treated with mastectomy, the use of radiation therapy is required for 4 or more positive lymph nodes and must be started after completion of chemotherapy; the use of radiation therapy is at the discretion of the investigator for 0-3 positive lymph nodes but, if used, must be started after the completion of chemotherapy * Prior to registration, the physician must designate if it is planned for the patient to receive radiation therapy (for adjuvant radiation therapy post-mastectomy or, less commonly, post-conservative therapy but not primary breast radiation as part of breast conserving treatment) * Willing and able to sign an informed consent * Gene amplified by FISH or strong positivity (3+) by HercepTest on central review; Note: The patient registers based on community HER-2 testing using FISH or IHC, AC chemotherapy is initiated; the tumor block or slides must be received =\< 2 weeks from time of registration to the North Central Cancer Treatment Group (NCCTG) Operations Office for central HER-2 testing Exclusion Criteria: * Any of the following: * Pregnant women * Nursing women * Women of childbearing potential or their sexual partners who are unwilling to employ adequate contraception (condoms, diaphragm, intrauterine device \[IUD\], surgical sterilization, or abstinence, etc.); hormonal birth control methods are not permitted * Locally advanced tumors (classification T4) at diagnosis including tumors fixed to chest wall, peau d'orange, skin ulcerations/nodules, or clinical inflammatory changes (diffuse brawny cutaneous induration with an erysipeloid edge) * Prior history of breast cancer, except LCIS * Bilateral invasive carcinoma, either metachronous or synchronous (EXCEPTION: Patients diagnosed with unilateral invasive carcinoma and metachronous or synchronous DCIS of the contralateral breast treated with mastectomy are eligible) * Prior chemotherapy, radiation therapy, immunotherapy, or biotherapy for breast cancer * Active, unresolved infection * Active cardiac disease * Any prior myocardial infarction * History of documented congestive heart failure (CHF) * Current use of digitalis or beta-blockers for CHF * Any prior history of arrhythmia or cardiac valvular disease requiring medications or clinically significant * Current use of medications for treatment of arrhythmias or angina pectoris * Current uncontrolled hypertension (diastolic \> 100 mmHg or systolic \> 200 mmHg) * Clinically significant pericardial effusion * Prior anthracycline or taxane therapy for any malignancy * Sensitivity to benzyl alcohol * Neurology/Neuropathy-Sensory \>= grade 2 per the National Cancer Institute's (NCI's) Common Toxicity Criteria Version 2.0; EXCEPTION: Any chronic neurologic disorder will be looked at on a case-by-case basis by the study chair