Trastuzumab and Ixabepilone in Treating Women With HER2-Positive Metastatic Breast Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed invasive breast cancer, with stage IV disease * Tumors must be HER2 overexpressing; acceptable methods of measurement of HER2 expression include immunohistochemistry IHC) and fluorescence in situ hybridization (FISH); tumors tested by IHC must be 3+ positive for HER2 overexpression; tumors tested by FISH must be positive by the specific FISH assay for genetic amplification of HER2; tumors that are 3+ by IHC, but negative by FISH assay are ineligible; consideration should be given to performing a repeat biopsy, with reanalysis for HER2 overexpression, in patients who have received prior trastuzumab, as little data exist on the persistence of HER2 overexpression after prior treatment with trastuzumab; biopsy in this circumstance, however, is not required * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral CT scan; the protocol will employ the RECIST criteria * Prior Therapy - Two cohorts of patients will be treated on this treatment regimen; the two cohorts are determined by prior therapy and are as follows: * Treatment Cohort 1: * Chemotherapy: metastatic breast cancer: Patients in treatment Cohort 1 may NOT have received prior chemotherapy or prior trastuzumab therapy for metastatic breast cancer; patients may have received prior hormonal therapy for metastatic breast cancer * Chemotherapy: early stage breast cancer: Patients in treatment Cohort 1 may have received prior chemotherapy and/or hormonal therapy for early stage breast cancer; patients must be at least 6 months from prior chemotherapy received in the adjuvant setting * Trastuzumab: Patients in treatment Cohort 1 may have received trastuzumab in the adjuvant setting, provided that trastuzumab therapy ended at least 12 months prior to study participation; patients may not have previously received trastuzumab in the metastatic setting * Radiation therapy: Patients in treatment Cohort 1 may have received prior radiation therapy in either the metastatic or early stage settings; radiation therapy must be completed at least 7 days prior to study participation * Hormonal therapy: Patients in treatment Cohort 1 may have received hormonal therapy (therapies) in the adjuvant or metastatic setting; patients must discontinue hormonal therapy 2 weeks prior to study participation; patients with overt disease progression on prior hormonal therapy are eligible without waiting two weeks after discontinuing hormonal therapy, but must discontinue hormonal treatments prior to study participation * Treatment Cohort 2: * Chemotherapy: metastatic breast cancer: Patients in treatment Cohort 2 may have received up to two prior chemotherapy regimens for metastatic breast cancer; prior trastuzumab or other biologic or immunologic therapies are not considered to be chemotherapeutic regimens unless they were administered in conjunction with a chemotherapeutic agent; patients may have received prior hormonal therapy for metastatic breast cancer * Chemotherapy: early stage breast cancer: Patients in treatment Cohort 2 may have received prior chemotherapy and/or hormonal therapy for early stage breast cancer; if adjuvant chemotherapy was completed less than 6 months prior to the diagnosis of metastatic disease, the adjuvant regimen will be considered one of the two possible metastatic regimens * Trastuzumab: Patients in treatment Cohort 2 must have received one prior trastuzumab-containing regimen either in the metastatic setting or in the adjuvant setting; if the trastuzumab was administered in the adjuvant setting, disease recurrence must have occurred within 12 months of completion of adjuvant therapy * Radiation therapy: Patients in treatment Cohort 2 may have received prior radiation therapy in either the metastatic or early stage settings; radiation therapy must be completed at least 7 days prior to study participation * Hormonal therapy: Patients in treatment Cohort 2 may have received hormonal therapy (therapies) in the adjuvant or metastatic setting; patients must discontinue hormonal therapy 2 weeks prior to study participation; patients with overt disease progression on prior hormonal therapy are eligible without waiting two weeks after discontinuing hormonal therapy, but must discontinue hormonal treatments prior to study participation * Life expectancy of greater than 6 months * ECOG performance status =\< 2 (Karnofsky \>= 60%) * Patients must have adequate organ and marrow function as defined below; laboratory tests should be completed within 14 days prior to registration; left ventricular ejection fraction (LVEF) may be determined by either echocardiography or nuclear scintigraphy (i.e. MUGA scan or RVG), and should be obtained within 28 days prior to registration * Absolute neutrophil count \>= 1,500/mm\^3 * Platelets \>= 100,000/mm\^3 * Total bilirubin =\< 1.5 X institutional upper limit of normal * ALT(SGPT) =\< 5 X institutional upper limit of normal * LVEF \>= 50% * Concurrent Therapy: patients may not receive concurrent hormonal therapy, chemotherapy, or radiation treatments while on study; patients requiring radiation therapy during protocol-based treatment will be taken off study; if patients develop intraparenchymal brain metastases while on treatment, but do not have evidence of other systemic progression, they will be allowed to resume treatment with the combination once their radiation has been completed; they will be allowed to continue trastuzumab therapy during radiation, at the treating physician's discretion; nevertheless, the date of discovery of the CNS disease will still be considered the date of disease progression; patients may receive concurrent bisphosphonate therapy (e.g. pamidronate) while on study; patients may not receive other experimental treatments while on study * The effects of BMS-247550 on the developing human fetus at the recommended therapeutic dose are unknown; for this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * Patient Registration and Data Submission: Patients will be registered by contacting and faxing the completed eligibility checklist and all pages of the consent form to the Quality Assurance Office of Clinical Trials (QACT) at the Dana-Farber Cancer Institute; please fax to 617-632-2295 or telephone at 617-632-3761; a research nurse, Kathryn Clarke, will be available at 617-632-3478 to answer any protocol-related questions; you many also contact the study coordinator, Keri Hannagan, at 617-632-5584 * Regular data submissions should be made to Dana-Farber Cancer Institute's QACT; please fax all data in a timely manner to the number above Exclusion Criteria: * Patients may not be receiving any other investigational antitumor agents * Patients with leptomeningeal carcinomatosis are excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events; patients with a history of brain metastases are eligible, providing that they have completed treatment for their brain metastases at least 1 week prior to enrollment, are asymptomatic from their brain metastases and are not taking steroids; screening for CNS disease is not required if patients do not have symptoms that might be related to CNS metastases; patients with such symptoms should be evaluated for the possibility of CNS disease prior to study participation * Patients with a history of grade 3 or 4 allergic reactions attributed to compounds of similar chemical or biologic composition to the agents used in the study are ineligible; patients with a history of severe Cremophor reactions should be excluded; patients who experienced grade 1 or 2 hypersensitivity reactions to prior trastuzumab or taxane therapies are eligible IF these reactions did not prevent previous administration of such agents; patients who were deemed inappropriate candidates for trastuzumab or taxane-based treatments based on their hypersensitivity reactions are not eligible * Received prior epothilone therapy * Grade 2 or greater neuropathy (neuromotor or neurosensory) * Received prior high dose chemotherapy with bone marrow transplant or peripheral blood stem cell support within 2 years of study entry * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because BMS-247550 and trastuzumab are agents which may have the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with these drugs, breastfeeding should be discontinued if the mother is treated on study * Because patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy, HIV-positive patients receiving anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with agents administered during the study