This phase II trial studies how well pegylated liposomal doxorubicin hydrochloride and carboplatin followed by surgery and paclitaxel work in treating patients with stage II-III breast cancer that does not have estrogen receptors, progesterone receptors, or large amounts of human epidermal growth factor receptor 2 (HER2)/neu protein (triple negative). Drugs used in chemotherapy, such as pegylated liposomal doxorubicin hydrochloride, carboplatin, and paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving pegylated liposomal doxorubicin hydrochloride and carboplatin before surgery may make the tumor smaller and reduce the amount of normal tissue that needs to be removed. Giving pegylated liposomal doxorubicin hydrochloride and carboplatin followed by surgery and paclitaxel may be an effective treatment for breast cancer.