Cisplatin and Paclitaxel With or Without Everolimus in Treating Patients With Stage II or Stage III Breast Cancer

OBJECTIVES: Primary * To determine the pathological complete response in patients with triple-negative, stage II or III breast cancer treated with neoadjuvant cisplatin and paclitaxel with or without everolimus. Secondary * To determine the safety profile of these treatment regimens. * To evaluate tumor response to these treatment regimens as measured by ultrasound before definitive surgery. * To evaluate the rate of breast conservation surgery after treatment with these regimens. * To determine treatment-mediated changes in cell cycle position, proliferation, and apoptosis as well as status, levels, and phosphorylation state of S6K, p53, p73, and p63 and select p53 family target genes before and after initiation of paclitaxel. * To isolate RNA and generate microarray data sets from pre- and post-treatment biopsy material to identify a pre-treatment gene signature that will predict response. * To isolate RNA and generate microarray data sets from pre- and post-treatment biopsy material to identify a change in gene signature after the first treatment that will predict response. * To isolate RNA and generate microarray data sets from pre- and post-treatment biopsy material to determine if previously established p63 and p73 gene signatures predict response to treatment. * To isolate RNA and generate microarray data sets from pre- and post-treatment biopsy material to determine if a change will be observed in p63 and p73 gene signatures between pre- and post-treatment biopsies. * To isolate RNA and generate microarray data sets from pre- and post-treatment biopsy material to determine if triple-negative breast cancers can be clustered into different subtypes on the basis of gene expression, given the size of the microarray data set that will be generated from this clinical trial and previous clinical trials (\> 100 tumors). * To isolate RNA and generate microarray data sets from pre- and post-treatment biopsy material to determine if p63 and p73 gene signatures can sub-classify triple-negative breast cancers. OUTLINE: This is a multicenter study. Patients are stratified according to initial lymph node status (positive vs negative involvement) and tumor grade (low or intermediate vs high). Patients are randomized to 1 of 2 treatment arms. * Arm I: Patients receive cisplatin IV over 1 hour and oral everolimus once weekly in weeks 1-12 and paclitaxel IV over 1 hour once weekly in weeks 4-12 in the absence of disease progression or unacceptable toxicity. * Arm II: Patients receive cisplatin IV over 1 hour and oral placebo once weekly in weeks 1-12 and paclitaxel IV over 1 hour once weekly in weeks 4-12 in the absence of disease progression or unacceptable toxicity. Approximately 3-6 weeks after the completion of neoadjuvant therapy, patients undergo partial or total mastectomy with lymph node evaluation. Patients may then receive additional chemotherapy or radiotherapy. Patients undergo ultrasound-guided core biopsies at baseline and in weeks 1, 4, and 12 for analysis of proliferation, apoptosis, and pathway activity markers via IHC or western blotting and RNA microarrays. Patients are followed up within 3 weeks after surgery.