Melphalan/HDS followed by Physician's choice of SOC (eribulin, vinorelbine, or capecitabine)

The goal of this clinical trial is to learn if using a liver-directed therapy with high dose chemotherapy followed by approved cancer treatment to treat patients with breast cancer that has spread to the liver is safe and tolerable. The clinical trial will also learn if the liver-directed therapy with high dose chemotherapy works on the disease in the liver. Investigators will compare the use of the liver-directed therapy with high dose chemotherapy followed by approved cancer treatment or approved cancer treatment alone. Participants will: * Undergo up to two cycles of liver-directed therapy with high dose chemotherapy procedures followed by approved cancer treatment or take approved cancer treatment alone * Visit clinic at least every two weeks for checkups and tests * Complete scans approximately every 8 weeks