A First in Human Dose Escalation of Dendritic Cell Vaccine (DCV)

Inclusion Criteria: * Histologically or cytologically confirmed diagnosis of TNBC or HER2+BC per ASCO/CAP guidelines . A tumor can be considered a TNBC if the ER or PR is \<10%. * Trial participants must have a diagnosis of LMD. They must have the presence of malignant cells in the CSF (CSF+; note now cytology is considered diagnostic of LMD if the cytology is read as positive or suspicious; OR characteristic radiographic abnormalities (see below) of LMD). Signs and symptoms of LMD in and of themselves are not sufficient for inclusion. * Patients must have an Eastern Cooperative Oncology Group performance scale of ≤ 3. * Coincident Brain or Spinal cord metastases are allowed if these are stable and do not require local therapy at the time of enrollment. Individuals with previously treated stable Brain metastases are eligible to participate. * Stereotactic Radiosurgery (SRS) and/or prior radiotherapy is permitted \> 2 weeks prior to initial Dendritic Cell (DC) vaccine dose. A follow up brain MRI should be obtained prior to DC vaccine to determine stability of the lesions. An interval of at least 4 weeks after the end of whole brain radiation or for any surgical resection of brain lesions is permitted. * Life expectancy of ≥ 8 weeks. * Demonstrate adequate organ function as defined in protocol. All screening labs should be performed with 14 days of treatment initiation. * Provision of signed and dated informed consent form. * Corticosteroids at doses equivalent to 8 mg dexamethasone daily for symptom control are acceptable. This should be minimized wherever possible. * If the disease has progressed on current treatment in the CNS prior to consent, patients may continue current systemic cancer therapies as per PI discretion (Systemic Therapies Allowed) and Exclusion Criteria. Patients should not start a new anti-cancer agent until the 28 day safety period is completed. * Patients with systemic disease are eligible and will be managed as detailed in Section 6.3.1. * Pregnancy test: negative serum or urine pregnancy test at screening for women of childbearing potential. Must be repeated once-monthly during treatment. Contraception: Highly effective contraception for both male and female subjects throughout the study and for at least 90 days after last treatment administration, if the risk of conception exists. * The patient has an Ommaya reservoir or equivalent device which allows routine access to CSF and administration of DC1s. Exclusion Criteria: * Receiving other treatments specifically administered to treat LMD within the last 2 weeks or 5 half-lives of the agent, whichever is less. However, all other treatments to control systemic disease or bulk CNS disease will be eligible, provided the therapy is not a phase I agent, an agent which significantly and unequivocally penetrates the CSF (e.g., high-dose methotrexate, thiotepa, high-dose ara-C) per PI discretion. * The use of any immunotherapy within the last four weeks. * Patients with a ventriculoperitoneal or ventriculoatrial shunt must have an on/off device in their shunt systems to be eligible for the study. Patients must be able to tolerate shunt closure for \~4 hours without development of clinical signs of increased intracranial pressure. Patients unable to tolerate shunt closure for \~4 hours will not be eligible for the study. * Unable or unwilling to have a contrast-enhanced brain MRI. * Known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin,squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy. * Has an active infection requiring systemic therapy which in the opinion of the investigator will increase the risk to the patient. * Had major surgical procedure, or significant traumatic injury within two weeks. Ommaya placement is allowed. * Has a history of current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 90 days after the last dose of trial treatment. * Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1, 2 antibodies). Testing is not mandatory. * Has known active or chronic hepatitis B (HBV) or hepatitis C virus (HCV). Testing is not mandatory. * ORGAN TRANSPLANTATION: Prior organ transplantation including allogenic stem-cell transplantation. * Other severe acute or chronic medical conditions or psychiatric conditions including recent (within the past year) or active suicidal ideation or behavior; or laboratory abnormalities that may increase the risk associated with study participation or study treatment administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for entry into this study. * Has received a blood transfusion in the two weeks prior to leukapheresis. * Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist®) are live attenuated vaccines and are not allowed. Current COVID vaccines are not live vaccines.