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 (metastatic). FASN inhibitor TVB-2640 may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Trastuzumab is a form of targeted therapy because it attaches itself to specific molecules (receptors) on the surface of cancer cells, known as HER2 receptors. When trastuzumab attaches to HER2 receptors, the signals that tell the cells to grow are blocked and the cancer cell may be marked for destruction by the body's immune system. 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. Estrogen can cause the growth of breast cancer cells. Drugs used in endocrine therapy either lower the amount of estrogen made by the body or blocks the use of estrogen by the tumor cells. This may help stop the growth of tumor cells that need estrogen to grow. Giving FASN inhibitor TVB-2640 and trastuzumab in combination with paclitaxel or endocrine therapy may help control the disease in patients with HER2 positive breast cancer.