Subject has received or plans to receive the following excluded therapy/treatment prior to leukapheresis or lymphodepleting chemotherapy. Required Wash-out periods: Subject has anticipated life expectancy > months prior to leukapheresis and > months prior to lymphodepletion. No prior anti-leukemic therapy except the following are allowed: < week of corticosteroids, or hydroxyurea or emergent leukapheresis; longer steroid use for diseases other than leukemia is permitted DONOR: Deemed unable to undergo marrow harvesting or PBSC mobilization and leukapheresis Must be willing and able to accept at least three leukapheresis procedures Use of any of the following:\r\n* Therapeutic doses of corticosteroids (defined as > mg/day prednisone or equivalent) within days prior to leukapheresis; physiologic replacement, topical, and inhaled steroids are permitted\r\n* Allogeneic hematopoietic stem cell transplantation (Allo-HSCT) within days of leukapheresis\r\n* Cytotoxic chemotherapeutic agents within week of leukapheresis; oral chemotherapeutic agents are allowed if at least half-lives have elapsed prior to leukapheresis\r\n* Low dose chemotherapy (e.g., bortezomib, lenalidomide, cyclophosphamide ? mg/m^) given after leukapheresis to maintain disease control must be stopped ? days prior to initiation of lymphodepleting chemotherapy\r\n* Lymphotoxic chemotherapeutic agents within weeks of leukapheresis\r\n* Experimental agents within weeks of leukapheresis unless progression is documented on therapy and at least half-lives have elapsed prior to leukapheresis\r\n* Daratumumab or any other anti-CD monoclonal antibody therapy within days of leukapheresis Treatment with alemtuzumab within months prior to leukapheresis, or treatment with clofarabine or cladribine within months prior to leukapheresis Use of any of the following:\r\n* Therapeutic doses of corticosteroids (defined as > mg/day prednisone or equivalent) within days prior to leukapheresis; physiologic replacement, topical, and inhaled steroids are permitted\r\n* Allogeneic hematopoietic stem cell transplant (allo-HSCT) within days of leukapheresis\r\n* Cytotoxic chemotherapeutic agents within week of leukapheresis; oral chemotherapeutic agents are allowed if at least half-lives have elapsed prior to leukapheresis\r\n* Low dose chemotherapy (e.g., bortezomib, lenalidomide, cyclophosphamide =< mg/m^) given after leukapheresis to maintain disease control must be stopped >= days prior to initiation of lymphodepleting chemotherapy\r\n* Lymphotoxic chemotherapeutic agents within weeks of leukapheresis\r\n* Experimental agents within weeks of leukapheresis unless progression is documented on therapy and at least half-lives have elapsed prior to leukapheresis Must be willing and able to accept at least three leukapheresis procedures Subject has anticipated life expectancy > months prior to leukapheresis and > months prior to lymphodepletion. CRITERIA FOR LEUKAPHERESIS AND PRE-THERAPY EVALUATION Screening evaluation appropriate for leukapheresis and T-cell collection CRITERIA FOR SCREENING: Any known contraindication to leukapheresis CRITERIA FOR LEUKAPHERESIS AND PRE-THERAPY EVALUATION: Use of any of the following:\r\n* Cytotoxic or lymphotoxic agents (including prednisone > mg/day or equivalent corticosteroid) within week prior to leukapheresis; physiologic corticosteroid replacement, and topical or inhaled corticosteroids are not excluded\r\n* GVHD therapies within weeks prior to leukapheresis (e.g., calcineurin inhibitors, methotrexate or other chemotherapeutics, mycophenolate, rapamycin, thalidomide, immunosuppressive antibodies such as anti-TNF, anti-IL-, or anti-IL-R)\r\n* Experimental agents within weeks prior to leukapheresis unless progression is documented on therapy and at least half-lives have elapsed prior to leukapheresis\r\n* Radiation within weeks prior to leukapheresis unless there is progressive disease in irradiated lesions or there are additional non-irradiated, positron emission tomography (PET)-positive lesions \r\n* Allo-HSCT within days prior to leukapheresis or donor lymphocyte infusion (DLI) within weeks prior to leukapheresis\r\n* Treatment with cladribine within months prior to leukapheresis\r\n* Treatment with alemtuzumab within months prior to leukapheresis Adequate vascular access for leukapheresis procedure Treatment with alemtuzumab within months of leukapheresis or fludarabine or cladribine within months of leukapheresis Experimental agents within weeks of leukapheresis unless no response or disease progression is documented on the experimental therapy and at least half-lives have elapsed prior to leukapheresis Any condition contraindicating leukapheresis. Must be willing and able to accept two leukapheresis procedures Patients must be willing to provide at least mL, and up to mL, of whole blood obtained by phlebotomy and/or consent to leukapheresis for DC generation. Known exclusion criteria for leukapheresis, JCAR, or durvalumab therapy EXCLUSION CRITERIA FOR LEUKAPHERESIS AND PRE-THERAPY EVALUATION: Screening evaluation appropriate for leukapheresis and T-cell collection INCLUSION CRITERIA FOR TNBC: Patients must be off chemotherapy for a minimum of weeks prior to planned leukapheresis Must be willing and able to accept the leukapheresis procedure Patients must be willing to undergo two leukapheresis procedures for the investigational component of this trial Patient may be required to undergo leukapheresis (depending on the study phase/cohort) and must agree to leukapheresis if so assigned DONOR: Capable of undergoing leukapheresis Research participants' last dose of prior chemotherapy or radiation must be >= weeks before leukapheresis; Note: this criterion is not applicable if the research participant's donor is undergoing leukapheresis The last dose of prior chemotherapy, immunotherapy or radiation must be at least weeks before the leukapheresis procedure The last dose of investigational agents must be at least weeks before leukapheresis procedure unless no response or disease progression is documented on the experimental therapy and at least half-lives must have elapsed prior to leukapheresis If research participant is undergoing leukapheresis, he/she must be at least weeks from having received the last dose of immunosuppressant medications\r\n* Exceptions:\r\n** Steroids and tyrosine kinase inhibitors are allowed up to days prior to leukapheresis\r\n** Research participant cannot be on more than mg prednisone or equivalent doses of other corticosteroids at the time of leukapheresis If research participant is undergoing leukapheresis the last dose of prior chemotherapy, immunotherapy or radiation must be at least weeks before the leukapheresis procedure\r\n* Exception rule: the wash out period for Hydrea is hours ELIGIBILITY TO UNDERGO LYMPHODEPLETION:\r\n* Please note that none of these criteria are applicable of the research participant's donor is undergoing leukapheresis Must be willing and able to accept at least two leukapheresis procedures Patients must be willing to provide at least mL, and up to mL, of whole blood obtained by phlebotomy and/or consent to leukapheresis for DC generation. Availability of production capacities for the patient's IMA product prior to the leukapheresis TREATMENT SCREENING: Any condition contraindicating leukapheresis DONOR: Able and willing to undergo leukapheresis DONOR: Individuals deemed unable to undergo marrow harvesting or PBSC mobilization and leukapheresis Subject who has had cytotoxic chemotherapy within weeks prior to leukapheresis; immune therapy or biological therapy within weeks prior to leukapheresis; corticosteroids or any other immunosuppressive therapy within weeks prior to leukapheresis; tyrosine kinase inhibitor (TKI) (e.g. erlotinib, gefitinib) and any other anti-cancer treatment within week prior to leukapheresis. Investigational treatment within weeks prior to leukapheresis; experimental anti-cancer vaccine within months prior to leukapheresis in the absence of response or in the opinion of the Investigator is responding to an experimental vaccine given within months prior to leukapheresis; any prior gene therapy using an integrating vector. Unwilling to undergo two leukapheresis procedures; if patients are unable to undergo the leukapheresis procedures, then a -cc blood draw (green heparinized tubes) is permitted in place of the leukapheresis Patients with medical conditions precluding leukapheresis Must be willing and able to accept two leukapheresis procedures Must be willing and able to accept at least two leukapheresis procedures Emergency leukapheresis Treatment with alemtuzumab within months prior to leukapheresis, or treatment with clofarabine or cladribine within months prior to leukapheresis Emergency leukapheresis; Use of any of the following medications or treatments within the noted time prior to leukapheresis: Alemtuzumab within months prior to leukapheresis Cladribine within months prior to leukapheresis Fludarabine within weeks prior to leukapheresis Cyclophosphamide, ifosfamide, bendamustine, chlorambucil, or melphalan within weeks prior to leukapheresis Venetoclax within days prior to leukapheresis Idelalisib within days prior to leukapheresis Lenalidomide within day prior to leukapheresis Experimental agents, including off-label use of approved drugs, within weeks prior to leukapheresis unless progression is documented on the experimental therapy and at least half-lives have elapsed prior to leukapheresis Having received systemic immune suppressive therapy within days prior to leukapheresis Patients may receive hydroxyurea, steroids, or leukapheresis as necessary until day of treatment DONOR: Alternatively to a fresh unmodified leukapheresis product, previously collected cryopreserved peripheral blood stem cells (PBSC) after mobilization with G-CSF or cryopreserved unmodified leukapheresis product from the original donor can be used; if cryopreserved product is not available, the following criteria apply for the DLI product: Steroids: Therapeutic doses of corticosteroids are prohibited within days prior to leukapheresis. Chemotherapies: Salvage chemotherapy must be stopped at least week prior to leukapheresis Treatment with alemtuzumab within months prior to leukapheresis, or treatment with clofarabine or cladribine within months prior to leukapheresis Donor must be able to undergo leukapheresis DONOR: Able and willing to undergo leukapheresis CRITERIA FOR LEUKAPHERESIS: Known infection with hepatitis B virus (HBV) and hepatitis C virus (HCV); (if a patient was not tested at the time of their leukapheresis, they must be tested prior to receiving T cell infusion; if testing was done for leukapheresis, this is adequate and does not need to be repeated) Patients may receive hydroxyurea, steroids, or leukapheresis as necessary until day of treatment Leukapheresis; Treatment with alemtuzumab within months of leukapheresis, or treatment with fludarabine or cladribine within months of leukapheresis Experimental agents within weeks of leukapheresis unless no response or disease progression is documented on the experimental therapy and at least half-lives have elapsed prior to leukapheresis. GVHD therapies within weeks of leukapheresis and JCAR administration. Radiation within weeks of leukapheresis. Inability to undergo leukapheresis Patients may receive anagrelide for up to days (in countries where the product is registered). Leukapheresis is allowed up to hours prior to the first treatment cycle with omacetaxine. Leukapheresis ? weeks prior to starting CC-.