Trastuzumab With or Without Everolimus in Treating Women With Breast Cancer That Can Be Removed By Surgery

DISEASE CHARACTERISTICS: * Histologically confirmed diagnosis of invasive breast cancer * Previously untreated disease * Candidate for breast-conserving surgery, as defined by both of the following: * Clinical stage cT1-3, cN0-2 disease * Clinical stage M0 disease (bone scan, chest X-ray, and liver ultrasound required at screening to exclude metastatic disease) * HER2-positive primary tumor, defined as meeting either of the following criteria: * IHC 3+ * IHC 2+ and FISH positive (centralized confirmation) * No inflammatory breast cancer or bilateral breast cancer * Patients who have been treated for cancer of the contralateral breast can be included if there is at least a 5 year time interval from last systemic treatment for breast cancer before randomization into this study * Hormone receptor status not specified PATIENT CHARACTERISTICS: * WHO performance status 0-1 * Menopausal status not specified * WBC ≥ 3.5 x 10\^9/L * ANC ≥ 1.5 x 10\^9/L * Platelet count ≥ 100 x 10\^9/L * Hb ≥ 10 g/dL * Serum bilirubin ≤ 1.5 times upper limit of normal (ULN) * Serum transaminases activity ≤ 2.5 times ULN * Alkaline phosphatase ≤ 2.5 times ULN * Creatinine ≤ 1.5 mg/dL OR creatinine clearance ≥ 60 mL/min * FEV \> 55% by MUGA or ECHO * Spirometry and DLCO \> 50% of normal * O\_2 saturation \> 88% at rest on room air * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No known hypersensitivity to everolimus, sirolimus, trastuzumab (Herceptin®), or lactulose * No hypercholesterolemia/hypertriglyceridemia ≥ grade 3 * No hypercholesterolemia/hypertriglyceridemia ≥ grade 2 with history of coronary artery disease (despite lipid-lowering treatment if given) * No uncontrolled infection * No other concurrent severe and/or uncontrolled medical disease which could compromise participation in the study, including any of the following: * Uncontrolled hypertension * Congestive cardiac failure * Ventricular arrhythmias * Active ischemic heart disease * Myocardial infarction within the past year * Chronic liver or renal disease * Active gastrointestinal tract ulceration * Severely impaired lung function * No known history of HIV seropositivity * No psychological, familial, sociological, or geographical condition potentially hampering compliance with the study protocol and follow-up schedule * Willing to participate in the biological investigations * Not deprived of liberty or placed under guardianship * Patients must be affiliated to a Social Security System PRIOR CONCURRENT THERAPY: * See Disease Characteristics * More than 30 days (from the screening visit) since prior other investigational drugs * More than 5 days (from randomization) since prior and no concurrent strong inhibitors or inducers of the isoenzyme CYP3A, including any of the following * Rifabutin * Rifampicin * Clarithromycin * Ketoconazole * Itraconazole * Voriconazole * Ritonavir * Telithromycin * No other concurrent anti-cancer treatments such as chemotherapy, immunotherapy/biological response modifiers, endocrine therapy, or radiotherapy