Combination Chemotherapy With or Without Trastuzumab in Treating Women With Metastatic Breast Cancer

Inclusion Criteria:

* Histologically confirmed adenocarcinoma of the breast with manifestations of metastatic progression
* HER2 expression status in primary breast tissue and/or site(s) of metastasis must be determined by the ECOG Pathology Coordinating Office; (these are the results that will be used at time of registration); NOTE: for this protocol, HER2/neu non-overexpressed status will be defined as 0 and 1+ scores using the DAKO HercepTest; HER2 overexpressed status will be defined as 2+ score (if confirmed amplified by FISH) or 3+ score using the DAKO HercepTest
* Cytologically positive pleural or peritoneal effusions are considered evaluable disease provided local intra-cavitary treatment is not introduced at the onset of therapy; to be considered as evaluable disease, pleural effusions may not have been previously drained or sclerosed
* Blastic or mixed blastic/lytic osseous metastases only are evaluable disease provided they are accompanied by an analgesic requirement or a decrease in performance status, and will not require radiation treatment within two cycles from the start of protocol; pure osteolytic disease is evaluable; bone disease must be x-ray proven for the site to be evaluable; patients whose only evidence of metastatic disease is an abnormal bone scan without confirmatory x-rays are not eligible for this study
* No prior chemotherapy for advanced disease; prior adjuvant chemotherapy (including taxanes) allowed, if completed \> 6 months before the diagnosis of metastatic disease; no prior adjuvant anthracycline, nor any prior exposure to other anthracycline- (e.g., epirubicin, any liposomal doxorubicin formulation), nor any anthracenedione- (e.g., mitoxantrone) containing regimen allowed; no prior therapy with Herceptin allowed; NOTE: chemotherapy after ipsilateral breast recurrence following breast conservation surgery would not be considered chemotherapy for advanced disease; however, in post-mastectomy patients chemotherapy for local/regional recurrence is considered treatment for advanced disease
* No prior radiotherapy other than to the conserved breast, to the post-mastectomy chest wall, or to a limited field involving \< 25% of marrow-containing bone; NOTE: previous post-mastectomy radiation therapy involving chest wall ± internal mammary lymph node chain (IMN) is allowed; however, patients who received photon IMN treatment are ineligible; NOTE: radiotherapy must be completed \>= 2 weeks prior to registration; it may not be given concurrently with Doxil, Taxotere, or Herceptin
* Prior hormonal therapy in either a metastatic or adjuvant setting is allowed, but patients must have been off such therapy for \>= 2 weeks prior to registration
* Disease-free of prior non-breast invasive malignancies for \>= 5 years with the exception of curatively-treated basal cell or squamous cell carcinoma of the skin or carcinoma in situ of the cervix
* ECOG performance status of 0, 1, or 2
* At least two weeks after any major surgery (including mastectomy) and recovered from all toxicity
* Creatinine =\< 1.5 mg/dl
* Granulocytes \>= 1,500/mm³
* Platelets \>= 100,000/mm³
* SGOT(AST) =\< 2.5 x the upper limit of normal
* Bilirubin within normal limits for institution
* No history of deep venous thrombosis, pulmonary thromboembolism, or other thromboembolic condition
* Women must not be pregnant or breastfeeding; the effect of Herceptin to the fetus is unknown; Doxil is known to be harmful to the fetus
* Women of childbearing potential must be advised to use an accepted and effective method of contraception
* No patients with untreated brain metastasis or brain metastasis undergoing radiation or for whom brain metastasis represent the sole site of disease; patients with previously treated brain metastasis who have responded to brain radiotherapy and/or surgery and continue in response are eligible, provided the brain is not the only site of disease
* The left ventricular ejection fraction must be at or above the lower institutional limits of normal (as assessed by MUGA scan or echocardiogram obtained within six weeks prior to registration); patient will not be eligible if baseline LVEF assessment not performed
* No prior history of myocardial infarction, congestive heart failure, or arrhythmia requiring medication; no history of hypertension or systolic or diastolic dysfunction; no EKG evidence of ventricular hypertrophy, conduction abnormality, or serious arrhythmia; patient will not be eligible if baseline EKG assessment not performed within 4 weeks