This phase II trial studies how well FASN inhibitor TVB-2640, paclitaxel, and trastuzumab work in treating patients with HER2 positive breast cancer that has spread to other places in the body. FASN inhibitor TVB-2640 may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as paclitaxel and trastuzumab, 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 FASN inhibitor TVB-2640, paclitaxel, and trastuzumab may work better in treating patients with HER2 positive breast cancer.