SHARON: A Clinical Trial for Metastatic Cancer Using Chemotherapy and Patients' Own Stem Cells

Inclusion Criteria * Age ≥ 18 years. * Pancreatic or breast cancer, as described below. * Stage IV (based on AJCC staging guidelines) at the time of enrollment. a. Note that potential subjects with stage IV cancer that have had a complete response from prior chemotherapy are still potentially eligible. * Expected survival time ≥ 6 months, as determined by the investigator. * Life expectancy not severely limited by diseases other than malignancy, as determined by the investigator. * Karnofsky score ≥ 60%. * No chemotherapy within 2 weeks of enrollment. * Prior surgical resection or ablation of the primary tumor is allowed but not required. * If post-surgical, the subject must be at least 28 days post-op with the surgical wounds healed and significant complications resolved. * Potential subjects who have received previous chemotherapy and/or PARP inhibitors may be enrolled. * Measurable or non-measurable disease by the revised response evaluation criteria in solid tumors (RECIST) v.1.1. * For potential subjects with a germline BRCA1, BRCA2, or PALB2 mutation: a. The mutation must be known to be deleterious or suspected to cause functional impairment as assessed by a CLIA-certified laboratory according to the variant classification criteria described in the study protocol. * For potential subjects with somatic BRCA1, BRCA2, or PALB2 mutations: 1. The mutation must be a known or suspected deleterious mutation as assessed by a CLIA-certified laboratory according to the variant classification criteria described in the study protocol. 2. There must be biallelic loss or inactivation of the mutated BRCA1, BRCA2, or PALB2 gene as assessed by a CLIA-certified laboratory. 3. The Genetics Review Committee for this trial, which is comprised of a core group of investigators and whose actions are performed in accordance with the committee's charter, must agree that the biallelic mutations are deleterious or suspected deleterious. * For subjects without a BRCA1, BRCA2, or PALB2 mutation 1. Subject must have received at least 16 weeks of first-line (platinum-based\*) chemotherapy with no evidence of treatment failure, where treatment failure is defined as growing tumors, new lesions, or a steadily rising tumor marker during or within eight weeks of completion of the first line therapy. 2. \* Subjects can also have been treated with FOLFIRINOX but switched to FOLFIRI due to oxaliplatin side effects. * For potential subjects with pancreatic cancer: 1. Pancreatic ductal adenocarcinoma or pancreatic acinar cell carcinoma. 2. If the potential subject has had surgical resection of the primary tumor, then there must be no evidence of disease progression between the time of surgical resection of the primary tumor and screening for enrollment if the patient is seeking enrollment in the immediate post-surgery period. * For potential subjects with breast cancer: 1. Adenocarcinoma of the breast. 2. HER2-negative cancer as per American Society of Clinical Oncology/College of American Pathologists human epidermal growth factor receptor 2 (HER2) testing in breast cancer guidelines. 3. Male or female sex. * Histological or cytological confirmation of the primary cancer diagnosis is required. * Metastatic disease must be histologically or cytologically confirmed unless in the clinical judgment of the investigator a biopsy is not needed for diagnostic purposes. * Female participants of childbearing potential must agree to do one of the following from the time of signing of the informed consent through 6 months after the last dose of melphalan: 1. Simultaneously practice two effective barrier methods of contraception. Oral and injectable contraceptives are not allowed. Barrier methods of birth control (e.g., diaphragm and spermicide, or condom and spermicide) are required. 2. Practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods, and withdrawal) are not acceptable methods of contraception. * Male participants: 1. Unless the male is in a monogamous relationship with a female that does not have child-bearing potential, male subjects (even if surgically sterilized) must agree to do one of the following from the time of signing of the informed consent through 6 months after the last dose of melphalan: 1. Practice effective barrier contraception, plus a second method of effective contraception. 2. Practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods, and withdrawal) are not acceptable methods of contraception. Exclusion Criteria * Rapid disease progression or clinical features concerning for onset of rapid symptomatic deterioration, as determined by the investigator. * Biliary tract obstruction. * Current cholangitis. A biliary stent in situ does not otherwise exclude protocol participation. * A history of only one episode of cholangitis and fewer than 30 days have passed since discontinuation of antibiotic treatment. * A history of multiple episodes of cholangitis and after discussion between the site study team and sponsor medical monitor and careful evaluation for suitability the patient is deemed to be unsuitable for the trial due to risk of recurring cholangitis. * Portal hypertension. * Sinistral portal hypertension. * Obliteration or significant obstruction of the major veins or arteries (e.g., portal vein, superior mesenteric artery, superior mesenteric vein). * Clinically significant malignant ascites or malignant pleural effusion, as determined by the investigator. * Metastatic lesion to the heart or eye. * Chemotherapy for an indication other than treatment of the current cancer within the past 1 year with a more than 30% risk of recurrence as determined by the investigator. * Known or suspected metastati