Cisplatin, Paclitaxel, and Everolimus in Treating Patients With Metastatic Breast Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed invasive mammary carcinoma * Stage IV disease * Basal-like disease (triple-negative, hormone-refractory, HER2-negative) * No locally recurrent breast cancer * No symptomatic brain metastases * Patients with a history of brain metastases are eligible provided they are clinically stable for \> 3 weeks after completion of radiotherapy and are not taking steroids or therapeutic anticonvulsants that are cytochrome P450 3A4 (CYP3A4) modifiers * Patients with asymptomatic brain metastases are eligible provided they are not taking prophylactic anticonvulsants that are CYP3A4 modifiers PATIENT CHARACTERISTICS: * Pre- or post-menopausal * European Cooperative Oncology Group (ECOG) performance status 0-1 * Life expectancy ≥ 6 months * Absolute neutrophil count (ANC) ≥ 1,000/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Creatinine ≤ 1.5 times upper limit of normal (ULN) * Total bilirubin ≤ 1.5 times ULN (≤ 3 times ULN in the presence of liver metastasis) * Direct bilirubin will be measured in patients with Gilbert syndrome * serum glutamate oxaloacetate transaminase (SGOT) and serum glutamate pyruvate transaminase (SGPT) ≤ 1.5 times ULN (≤ 3 times ULN in the presence of liver metastasis) * Alkaline phosphatase ≤ 3 times ULN (in the presence of liver metastasis) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective barrier contraception during and for 3 months after completion of study treatment * Able to swallow and retain oral medication * No malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel * No concurrent uncontrolled illness including, but not limited to, any of the following: * Ongoing or active infection requiring parenteral antibiotics * Impaired lung function (chronic obstructive pulmonary disease or lung conditions requiring oxygen therapy) * New York Heart Association class III-IV congestive heart failure * Unstable angina pectoris, angioplasty, stenting, or myocardial infarction within the past 6 months * Uncontrolled hypertension (systolic BP \> 180 mm Hg or diastolic BP \> 100 mm Hg, found on 2 consecutive measurements separated by a 1-week period and despite adequate medical support) * Clinically significant cardiac arrhythmia (multifocal premature ventricular contractions, bigeminy, trigeminy, ventricular tachycardia that is symptomatic or requires treatment \[grade 3 according to NCI Common Toxicity Criteria for Adverse Events v3.0\]) * Uncontrolled diabetes (hyperosmolar state, ketoacidosis, etc.) * Psychiatric illness or social situations that would compromise patient safety or limit compliance with study requirements including maintenance of a compliance/pill diary * No symptomatic neuropathy ≥ grade 2 * No other invasive cancer within the past 5 years except for completely resected basal cell or squamous cell carcinoma of the skin or successfully treated cervical carcinoma in situ * No hypersensitivity to paclitaxel or drugs using the vehicle Cremophor, Chinese hamster ovary cell products, or other recombinant human antibodies * No history of hepatitis B or C PRIOR CONCURRENT THERAPY: * See Disease Characteristics * Recovered from prior therapy * Prior total cumulative life-time dose of doxorubicin ≤ 360 mg/m\^2 or epirubicin ≤ 640 mg/m\^2 * No more than 4 prior chemotherapy treatments in the metastatic setting (not including endocrine therapy or single-agent biologic therapy) * At least 2 weeks since prior investigational drugs * At least 14 days since prior and no concurrent herbal or dietary supplements * At least 14 days since prior and no concurrent CYP3A4 inducers * At least 7 days since prior and no concurrent CYP3A4 inhibitors * Concurrent radiotherapy to painful bone metastases or areas of impending bone fracture allowed provided radiotherapy is initiated before study entry * No other concurrent anticancer therapy (chemotherapy, radiotherapy, surgery, immunotherapy, hormonal therapy, biologic therapy)