This trial studies how well paclitaxel, trastuzumab, and pertuzumab work in eliminating further chemotherapy after surgery in patients with HER2-positive stage II-IIIa breast cancer who have no cancer remaining at surgery (either in the breast or underarm lymph nodes) after pre-operative chemotherapy and HER2-targeted therapy. Drugs used in chemotherapy, such as 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. Trastuzumab and pertuzumab are both a form of "targeted therapy" because they work by attaching themselves to specific molecules (receptors) on the surface of tumor cells, known as HER2 receptors. When these drugs attach to HER2 receptors, the signals that tell the cells to grow are blocked and the tumor cell may be marked for destruction by the body's immune system. Giving paclitaxel, trastuzumab, and pertuzumab may enable fewer chemotherapy drugs to be given without compromising patient outcomes compared to the usual treatment.