This phase II trial studies how well T-DMI with or without abemaciclib works for the treatment of HER2-positive breast cancer that has spread to other places in the body (metastatic). T-DM1 is a monoclonal antibody, called trastuzumab, linked to a chemotherapy drug called DM1. Trastuzumab attaches to HER2 positive cancer cells in a targeted way and delivers DM1 to kill them. Abemaciclib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving T-DM1 and abemaciclib may work better in treating patients with breast cancer compared to T-DM1 alone.