This phase II trial studies how well pertuzumab, trastuzumab, and paclitaxel albumin-stabilized nanoparticle formulation work in treating patients with human epidermal growth factor receptor (HER) 2-positive stage II-IV breast cancer. Monoclonal antibodies, such as pertuzumab and trastuzumab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Drugs used in chemotherapy, such as paclitaxel albumin-stabilized nanoparticle formulation, work in different ways to kill tumor cells or stop them from growing. Giving pertuzumab and trastuzumab together with paclitaxel albumin-stabilized nanoparticle formulation may be a better way to block tumor growth.