Combination Chemotherapy and Peripheral Blood Stem Cell Transplant Followed By Aldesleukin and Sargramostim in Treating Patients With Inflammatory Stage IIIB or Metastatic Stage IV Breast Cancer

Inclusion Criteria: Patients with inflammatory (stage IIIb) or responsive stage IV breast cancer with metastasis to soft tissue and/or bone; responsive stage IV disease is defined as patients who achieve a PR (>= 50% reduction in measurable tumor burden) or CR following initial chemotherapy for metastatic disease or patients with locally recurrent disease (chest wall/axillary nodes) who are rendered disease-free following surgery or radiation therapy without receiving chemotherapy; bone disease is categorized as responsive if there is demonstrated sclerosis of prior lesions with no new lesions Patients should have received 4-7 cycles of an Adriamycin and/or taxane-based regimen for stage IIIb or stage IV disease; locally recurrent (chest wall/axillary nodes) patients rendered NED by RT or surgery do not need to receive chemotherapy for stage IV disease prior to Cytoxan/Taxol Patient has received Cytoxan 4 gm/m^2 x 1 and Taxol 250 mg/m^2 x 1 per FHCRC protocol 506.03; Cytoxan/Taxol must be given after all other chemotherapy is completed and before transplant Stem cells were collected after mobilization with Cytoxan/Taxol or after mobilization from an FHCRC approved cytokine protocol; if syngeneic collection, PBSC's were collected by using G-CSF according to FHCRC protocol 753; patient has an adequate number of peripheral blood stem cells stored (>= 2.5 x 10^6 CD34+ cells/kg) The patient must have the capacity to give informed consent; the patient must have signed an approved consent form conforming with federal and institutional guidelines Hepatic function: Bilirubin =< 2 mg%; SGOT or SGPT =< 2.5 x institutional normal Renal function: Creatinine =< 2.0 mg/dl or a creatinine clearance >= 50 mg/min Pre-Study tests have been performed as outlined in the Study Calendar Patients will begin IL-2/GM-CSF therapy if they meet the following criteria post-transplant: Can start therapy 30 to 100 days after transplant Karnofsky performance status > 60 ANC > 1,000 cells/mm^3 and platelets > 30,000/cells/mm^3 (transfusion independent) for at least 5 days before starting therapy Total bilirubin =< 2.5 x upper limit of normal SGOT =< 2.5 x upper limit of normal Creatinine =< 2.0 mg/dl Exclusion Criteria: Patients with a Karnofsky Performance Score less than 70 Patients with a left ventricular ejection fraction less than 50 % (LVEF must be performed in patients with symptoms of CHF, abnormal cardiac exam or history of Adriamycin therapy total dose > 400 mg/m^2) Patient is pregnant Patient is seropositive for the human immunodeficiency virus Patients with a history of seizures Patients with hypersensitivity to E.coli preparations Patients with active auto-immune disease Patients with clinically significant pulmonary disease, i.e., diffusion capacity corrected < 60% of predicted; patients with pulmonary problems should be evaluated with appropriate pulmonary studies and/or consult Patients with a history of CNS lesion (brain or carcinoid meningitis) Patients with significant active infection precluding transplant Patients who have had more than one prior chemotherapy regimen for stage IV disease or a prior transplant for any stage disease Patients who have had CD34+ selection of their PBSC products Patients will not receive IL-2/GM-CSF therapy if they: Are > 100 days from transplant Have documented disease progression after transplant Have an active infection Manifested cardiac complications during the initial transplant period, including arrhythmias (that required therapy), congestive heart failure, angina, myocardial infarct, or decreased LVEF to < 45% Currently have pericardial effusions, pleural effusions or ascites Manifested pulmonary toxicity during the initial transplant period and have a diffusion capacity corrected =< 60% Are on steroids Currently have a Grade 3 toxicity from BuMelTT If the patient does not wish to receive the therapy