Paclitaxel With or Without Trastuzumab in Treating Patients With or Without HER-2/Neu Breast Cancer That is Inoperable, Recurrent, or Metastatic

Inclusion Criteria:

* Histologically confirmed adenocarcinoma of the female breast which is inoperable, recurrent or metastatic
* HER-2/neu status must be known at the time of protocol registration; HER-2/neu assessment will be based on FISH analysis of either the primary tumor or a metastatic site; a scoring of 0 or 1+ by immunohistochemistry (IHC) is considered negative; 2+ is considered negative unless confirmed by FISH positivity, in which case it should be considered positive; 3+ by IHC is considered positive; for centers using FISH only, a positive FISH assay by itself is sufficient to determine HER-2 positivity
* Patients with the following prior therapy are eligible:

  * Patients with 0-1 prior chemotherapy regimens for metastatic or locally advanced breast cancer, with the following exception: no prior taxane for metastatic/locally advanced breast cancer
  * Patients with 0-1 prior chemotherapy regimens in the adjuvant setting; if adjuvant regimen included a taxane, patient must have been disease free for at least 12 months from completion of adjuvant therapy until relapse
  * Patients must be \> 2 weeks from prior surgery, other than simple biopsy or placement of venous access device; patients must be \> 4 weeks from prior chemotherapy; patients must be \>6 weeks from nitrosoureas, melphalan, or mitomycin

    * Patients must be \> 4 weeks from prior hormonal therapy unless tumor measurements document clear progression while on treatment; if progression is documented and toxicity from hormonal regimen has resolved, patients may be placed on study \> 1 week from prior hormonal therapy
* Prior Herceptin therapy is not allowed
* Patients with central nervous system metastases are eligible only if the patient has completed cranial irradiation at least 6 months prior, is currently asymptomatic, and is not currently receiving corticosteroids for this condition; patients with leptomeningeal carcinoma (carcinomatous meningitis) are not eligible
* MESURABLE DISEASE: Any mass reproducibly measurable in two perpendicular dimensions, examples include:

  * Pulmonary nodules
  * Hepatic lesions
  * Skin nodules (if two measurements can be assigned)
  * Lymph nodes
* The following lesions do not qualify as measurable:

  * Central nervous system (CNS) lesions
  * Bone disease only; lytic lesions should be documented and followed
  * Lymphangitic pulmonary metastases (patients with lymphangitic metastases are eligible if there are other sites of metastatic disease which can be measured)
  * Lesions which have been irradiated unless there is definite documentation of progression since radiotherapy
* A baseline assessment of left ventricular ejection fraction within 8 weeks of registration is required (echocardiogram or resting multi gated acquisition scan \[MUGA\] (radionuclide cineangiography \[RNCA\]) nuclear scintigraphy); patients with a left ventricular ejection fraction (LVEF) \< 45% are ineligible
* Granulocytes \>= 1500/ul
* Platelet count \>= 100,000/ul
* Creatinine =\< 2.0 mg/dl
* Bilirubin within institutional normal limits
* Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\])