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

Eligibility criteria -Maximum number of patients will include two-thirds of the patients in Arm 1 and one-third of the patients for Arm 2 (total of 145 patients). Estimated time for accrual with \~ 3 patients/month would be \~ 3.5 years. Inclusion criteria: * Patients must provide informed written consent. * Patient must be ≥ 18 years of age. * ECOG performance status 0-1. * Clinical stage II or stage III triple-negative (ER and/or PR no staining or weak staining in less than or equal to 10% cells by immunohistochemistry \[IHC\] and HER2-negative by Herceptest \[0, 1+\] or FISH) invasive mammary carcinoma, confirmed by histological analysis. * Patients who have measurable\* residual tumor at the primary site \*Measurable disease: any mass that can be reproducibly measured by physical examination, mammogram, and/or ultrasound and can be accurately measured in at least one dimension (longest diameter to be recorded) as 10 mm (1 cm), either in the breast or axillary lymph nodes. * Available core biopsies from the time of diagnosis. Fresh tissue must be obtainable at baseline or fresh tissue biopsy prior to treatment initiation. * Patients who will undergo surgical treatment with either segmental resection or total mastectomy. * Patients must have adequate hematologic, hepatic, and renal function. All tests must be obtained less than 4 weeks from study entry. This includes: * ANC \>/=1500/mm3 * Platelet count \>/=100,000/mm3 * Creatinine \</=1.5X upper limits of normal * Bilirubin, SGOT, SGPT \</=1.5X upper limits of normal\* \* for patients with Gilbert"s syndrome, direct bilirubin will be measured instead of total bilirubin. * The patient must have not had anyprior chemotherapy for primary breast cancer. * Patients with a prior history of contra-lateral breast cancer are eligible if they have no evidence of recurrence of their initial primary breast cancer within the last 5 years. * Able to swallow and retain oral medication. * Four days prior to biopsy procedures patients must be off medications that could increase risk of bleeding (i.e. ASA, NSAIDS, Coumadin, heparin products) * Potential subjects must complete all screening assessments as outlined in the protocol. * The pre-menopausal patient of childbearing potential must have had a negative pregnancy test and agreed to use birth control methods while participating in the study. Note: Women of childbearing potential and their male counterparts should use a barrier method of contraception during and for 3 months following protocol therapy. Ineligibility Criteria Exclusion Criteria: * Locally recurrent breast cancer. * Pregnant or lactating women. * Evidence of distant metastatic disease (i.e. lung, liver, bone, brain, etc.) * Use of CYP3A4 modifiers (Appendix A) * Serious medical illness that in the judgment of the treating physician places the patient at high risk of operative mortality. * Malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel. * History of other malignancy. Subjects who have been disease-free for 5 years, or subjects with a history of completely resected non-melanoma skin cancer or successfully treated in situ carcinomas are eligible. * History of hepatitis B or hepatitis C. If patient is judged to be at risk for having had exposure to viral B or C hepatitis (i.e. illicit IV drug use, blood transfusion prior to 1990, body piercing, tattoos, etc.), appropriate testing should be performed (i.e. Hepatitis B surface antigen antibody, and Hepatitis C antibody) * Active or uncontrolled infection requiring parenteral antibiotics. * Dementia, altered mental status, or any psychiatric condition that would prohibit the understanding or rendering of informed consent. * Symptomatic neuropathy (≥ grade 2). * Concurrent anti-cancer therapy (chemotherapy, radiation therapy, surgery, immunotherapy, hormonal therapy, or any other biologic therapy) other than the ones specified in the protocol. * Concurrent treatment with an investigational agent. * Used an investigational drug within 15 days or 5 half-lives, whichever is longer, preceding the first dose of randomized therapy.