Evaluation of the Safety and Efficacy of Treatment w/High Dose Melphalan Given Directly Into the Liver Followed by Treatment w/Approved Cancer Treatment or Approved Cancer Treatment Alone in Patients w/ Metastatic Breast Cancer w/Liver Dominant Disease

Inclusion Criteria: * Histologically confirmed diagnosis of MBC. * Patients with HER2-negative (IHC 0 or 1+ or 2+ and ISH non-amplified) MBC (including triple negative disease). * Patient with Hormone Receptor-Positive disease has progressed on or intolerant of prior endocrine therapy and CDK 4/6 inhibitors. * Disease progression after TOPO-1 isomerase inhibitor payload ADC, such as sacituzumab govitecan and/or trastuzumab deruxtecan. Patients not eligible or suitable for ADCs can be considered for this study. NOTE: In jurisdictions where those ADCs are not available as standard of care, patients will be eligible after prior treatment or intolerable toxicity on two standard chemotherapy regimens for the appropriate disease subtype. * Patient with HER2-negative breast cancer suitable for single agent chemotherapy as per judgement of treating investigator. * Patient is a suitable candidate for treatment with one of the following: eribulin, vinorelbine, or capecitabine as per judgement of treating investigator. * Patient has liver dominant metastatic disease. Liver-dominant is defined as the majority of total tumor burden is located in the liver, and/or the life-threatening component of the disease is located in the liver. * MBC metastases must involve ≤ 50% of the liver parenchyma. * If there is evidence of extrahepatic metastatic disease, it is limited, and the life-threatening component of disease is in the liver. Extrahepatic disease is restricted to lesions in the breast, lung, other visceral organs, lymph nodes and skin. * Disease in the liver must be measurable (per RECIST v1.1 guidelines) by computed tomography (CT) and/or magnetic resonance imaging (MRI). * Patient weighs ≥ 35 kg * Scans used to determine eligibility (CT scan of the chest/abdomen/pelvis and MRI of the liver) must be performed within 28 days prior to randomization. * Patient has an ECOG PS of 0-1. Exclusion Criteria: * Prior chemoembolization or radioembolization to the liver or prior hepatic arterial infusion therapy. * Evidence of clinically significant portal hypertension by history, endoscopy, or radiologic studies (large abdominal varices, prior history of varices by endoscopy). * New York Heart Association functional classification II, III or IV or active cardiac condition(s), including unstable coronary syndromes (unstable or severe angina, recent myocardial infarction), worsening or new-onset congestive heart failure, significant arrhythmias, or severe valvular disease that create(s) undue risks of undergoing general anesthesia. * History or evidence of clinically significant pulmonary disease that precludes the use of general anesthesia. * History of bleeding disorders, presence of brain metastases or other intracranial abnormalities that would put them at risk for bleeding with anti-coagulation. * Known varices at risk of bleeding, including medium or large esophageal or gastric varices, active peptic ulcer, or history of recent hemoptysis. * An active second malignancy or has a history of recent definitively treated invasive cancer within 2 years prior to enrolment. Exceptions are optimally treated and controlled basal cell carcinoma, other skin cancers, thyroid cancer. * Symptoms and signs indicating clinically significant progression of disease including cord compression, increasing pain symptoms, increasing oxygen requirements, impending pathological fracture, compressive lymphadenopathy, or symptomatic pleural effusion. * Pregnant or breastfeeding. * WOCBP (i.e., fertile meaning not permanently sterilized and having had a menstrual period within the past 12 months) who is unable to undergo hormonal suppression to avoid menstruation during treatment. * Patient requires chronic use of immunosuppressive drugs. NOTE: Oral prednisolone ≤ 10 mg/day or equivalent is allowed. * Unable to be temporarily removed from chronic anti-coagulation therapy. * Active bacterial infections with systemic manifestations (malaise, fever, leucocytosis). * An active infection, including Hepatitis B and Hepatitis C infection. NOTE: Patients with anti-hepatitis B core antibody (HBc) positive, or hepatitis B surface antigen (HBsAg) but DNA negative are allowed exception(s). * Known severe allergic reaction to iodine contrast that cannot be controlled by premedication with antihistamines and steroids. * History of or known hypersensitivity to melphalan or the components of the Melphalan/HDS system. * Known latex allergy. * History of known hypersensitivity to heparin or the presence of heparin-induced thrombocytopenia. * Uncontrolled endocrine disorder including diabetes mellitus, hypothyroidism, or hyperthyroidism. * Received anti-cancer therapy including radiotherapy or investigational agent for any indication ≤ 30 days prior to randomization. * Patients should have recovered to Grade 1 or less for AEs related to prior treatment unless deemed clinically not significant, such as lymphopenia, anemia, or grade 2 neuropathy due to prior taxane treatment. NOTE: Certain side effects that are unlikely to develop into serious or life-threatening events (e.g., alopecia) are allowed at ≥ Grade 1. * \< 28 days after surgery and surgical wound is not fully healed. * Currently under treatment for cancer other than MBC or is not deemed to be cancer free. * Not eligible to receive either eribulin or vinorelbine or capecitabine. * Albumin level \< 3.0 g/dL.