CARCIK CD123/33 for Refractory/Relapsed AML and BPDCN in Children and Adults

Inclusion Criteria: * Patients/ parents or legal representatives able and willing to provide written informed consent and to comply with the study protocol according to ICH and local regulations. Age-appropriate assent from children will also be requested. * Age limits: children (6 months - 17 years old) and adults (≥18 years old - 75 years old) * Subjects with active AML/BPDCN with evidence of tumor involvement in the bone marrow and/or peripheral blood as determined by morphology and flow cytometric analysis and for whom no curative treatment option exists using currently available therapies. Specifically: 1. AML/ BPDCN that has not achieved a CR, CRh, CRi, MLFS ELN criteria (1); partial remission or refractory disease (including primary refractory) after two or more lines of therapy are eligible. Or: 2. AML/ BPDCN relapsed following alloHCT (including AML evolved from myelodysplastic or myeloproliferative syndrome). Note: morphologic relapse is not required; persistent/recurrent disease-associated molecular phenotypic or cytogenetic abnormalities (measurable residual disease, MRD) with measurable disease in flow cytometry \> 1%, at any time after alloHCT is eligible. * Availability of an at least haploidentical (i.e. 4/8 HLA matched by allele typing) familial or unrelated donor willing to and eligible for blood or lymphocyte donation for the CARCIKCD123/33 cell production * Availability of a HCT donor, including a UCB, and patient eligible to a subsequent alloHCT * Confirmed expression of CD123 and CD33 on leukemic blasts by flow cytometry. * Prior treatment with anti-CD123- or anti-CD33-targeted therapy is permitted, provided a minimum washout period of 2 weeks has been completed before enrollment. * Eastern Cooperative Oncology Group (ECOG) performance status equal to 2 or less for subject ≥ 16 years of age, ore Lansky \>50 for subjects \< 16 years of age * Satisfactory organ functions: 1. Adequate cardiac and pulmonary function: ejection fraction (EF) by ECHO or MUGA \>40% 2. Adequate liver function: total bilirubin ≤ 2.0x ULN (≤ 3x ULN in patients with Gilbert's syndrome or documented liver involvement) and AST (aspartate aminotransferase)/ALT (alanine aminotransferase) 5x ULN. 3. Adequate renal function: creatinine ≤1.5x ULN or creatinine clearance (CrCl) calculated by Cockroft-Gault formula of ≥50 mL/min for adult patients in whom, in the Investigator's judgment, serum creatinine levels do not adequately reflect renal function. For children, (\<18 years) adequate renal function will be calculated using bedside Schwartz eGFR formula (eGFR \> 60 ml/min/1.73m2). * Life expectancy (in the opinion of the Investigator) of \> 12 weeks * Females of childbearing potential (FCBP) subjects must: 1. Have a negative pregnancy test as verified by the local investigator 2. Either commit to true abstinence from heterosexual contact or agree to use, and be able to comply with, effective contraception without interruption from screening until at least 12 months following CARCIKCD123/33 infusion and until CAR positive viable T cells are no longer present by quantitative polymerase chain reaction (qPCR) on two consecutive tests. 3. Contraception methods must include one highly effective method, like: surgical female sterilization, use of oral (estrogen and progesterone), injected, or implanted hormonal methods of contraception or placement of an intrauterine device (IUD) or intrauterine system (IUS), or other forms of hormonal contraception that have comparable efficacy (failure rate \<1%) 4. Agree to abstain from breastfeeding during study participation and for at least 12 months following V infusion and until CAR positive viable T cells are no longer present by quantitative polymerase chain reaction (qPCR) on two consecutive tests. * Male subjects must: 1. Practice true abstinence or agree to use a condom during sexual contact with a pregnant female or a female of childbearing potential for 12 months after following CARCIKCD123/33 infusion and until CAR positive viable T cells are no longer present by quantitative polymerase chain reaction (qPCR) on two consecutive tests. Exclusion Criteria: * Patients with clinically significant active viral, bacterial or fungal infection. * Patients with an active infection with Hepatitis B. However, patients with a controlled (treated) hepatitis will be allowed if the all the following criteria are met: 1. Anti-viral therapy for hepatitis B virus (HBV) must be given for at least 1 month prior to time of informed consent. 2. HBV viral load must be \<2000 IU/mL (104 copies/mL) prior to time of informed consent; and 3. those on active HBV therapy with viral load \<2000 IU/mL (104 copies/mL) should stay on the same anti-viral therapy throughout study treatment * Patients with an active hepatitis C virus (HCV) infection. However, patients with successfully treated chronic HCV infection will be allowed if they show a sustained virologic response at 12 weeks (SVR12) or 24 weeks (SVR24), and if there is a 4-week period between achieving sustained viral response (SVR12 or SVR24) and time of informed consent. * HIV Positive test (serology or PCR) * Rapidly progressive disease that in the estimation of the investigator and sponsor could affect compliance with the protocol or interpretation of results * Uncontrollable CNS leukemia or neurological symptoms defined as CNS grade 3. A CNS evaluation should be performed as clinically appropriated to rule out CNS involvement. * Presence of clinically meaningful donor specific anti-HLA antibodies (DSA) against CARCIK-CD123/33 donor haplotype HLA typing * Patients with another active invasive malignancy. Only patients with completely resected carcinoma in situ not requiring treatment other than surgery can be considered for treatment. * Class III/IV cardiovascular disability according to New York Heart Association (NYHA) classification, myocardial infarction or cerebrovascular accident within 30