Patients for whom the best available donor is mismatched at both HLA class I and class II Absence of donor specific HLA antibodies HLA typing prior to referral (consultation with HCT physician). If a subject has had HLA typing with accompanying documentation that full siblings were not HLA typed and that a search of the unrelated donor registry was not performed the subject will be considered eligible. Documentation will be reviewed and adjudicated by the Protocol Officer or his/her designee. DONOR: HLA mismatched or haploidentical related donors (including st degree relatives and half siblings)\r\n* The donor and recipient must be identical at least one allele of each of the following genetic loci: HLA-A, HLA-B, HLA-Cw, HLA-DRB, and HLA-DQB; a minimum match of / is therefore required, and will be considered sufficient evidence that the donor and recipient share one HLA haplotype DONOR: When more than one donor is available, the donor with the lowest number of HLA allele mismatches will be chosen, unless there is HLA cross-match incompatibility or a medical reason to select otherwise, in which case donor selection is the responsibility of the principal investigator (PI), in consultation with the immunogenetics laboratory; in cases where there is more than one donor with the least degree of mismatch, donors will be selected based on the most favorable combination of (i) HLA compatibility in cross-match testing and (ii) ABO compatibility; will prioritize the lowest number of mismatches in the host-versus-graft (HVG) direction (to potentially minimize graft rejection risk) DONOR: For a partially HLA-mismatched transplant, the patient must lack antibodies against donor HLA molecules; specifically, complement dependent cytotoxicity and flow cytometric crossmatch assays must be negative, and the mean fluorescence intensity (MFI) of any anti-donor HLA antibody by solid phase immunoassay should be < ; consult with Immunogenetics for the clinical significance of any anti-donor antibody; desensitization to remove anti-donor antibody should only be performed for patients who have no other donor options Patients with a related donor who is identical for one HLA haplotype DONOR: Related donors who are identical for one HLA haplotype Have evidence of recipient donor specific anti-HLA antibodies. HLA-haploidentical related donor (aged to years) Additional Patient Inclusion Criteria for Patients Assigned to Haploidentical BM Arm: Patients must be HLA typed at high resolution using DNA based typing at the following HLA-loci: HLA-A, -B, -C and DRB and have available a related haploidentical BM donor with , , or HLA-mismatches. A unidirectional mismatch in either the graft versus host or host versus graft direction is considered a mismatch. The donor and recipient must be HLA identical for at least one antigen (using high resolution DNA based typing) at the following genetic loci: HLA-A, HLA-B, HLA-C, and HLA-DRB. Fulfillment of this criterion shall be considered sufficient evidence that the donor and recipient share one HLA haplotype, and typing of additional family members is not required. Anti-donor HLA antibodies. Additional exclusion criteria: Presence of anti-donor HLA antibodies (positive anti-donor HLA antibody is defined as a positive cross-match test of any titer by complement-dependent cytotoxicity or flow cytometric testing or the presence of anti-donor HLA antibody to the high expression loci HLA-A, B, C, DRB, or DPB with mean fluorescence intensity (MFI) > by solid phase immunoassay). Recipient HLA antibodies against donor HLA Suitable related haploidentical donor identified:\r\n* Must be matched at least at of HLA antigens (A, B, C, DRB, DQ)\r\n* Must not be matched at more than of HLA antigens\r\n* Recipient should not have HLA antibodies to potential donor; if the recipient does have HLA antibodies to the potential donor, an alternative donor is preferred; however, if there are no suitable alternative donors, the donor to whom the patient has HLA antibodies can be utilized as long as the antibody titer is less than median fluorescence intensity (MFI); if the titer is > or = to MFI, the recipient must undergo successful antibody desensitization prior to enrollment on this study; any patients who have demonstrated donor specific antibodies will not be evaluated for the end points measured in this study but will be followed for treatment related toxicities\r\n* Haploidentical donors that are ABO compatible with the recipient are preferred; Minor ABO incompatibility is preferred to major ABO incompatibility; major ABO incompatibility between recipient and donor is the least preferred but still acceptable for this study\r\n* It is preferred that the haploidentical donor must be available to donate on day - and day at Roswell Park Cancer Institute (RPCI), so that fresh product can be processed by the RPCI stem cell lab and administered to the patient on day ; while less preferable, cryopreserved product may be utilized on this protocol Patients with donor specific HLA antibodies with a titer greater than MFI (whether or not they have undergone a desensitization protocol) Presence of donor directed HLA antibodies DONOR: Donor preference based on KIR/KIR ligand mismatch\r\n* In addition to HLA determination, KIR genotyping will be performed on potential donors; when more than one potential donor is available, preference will be given to the donor who demonstrates KIR incompatibility with recipient HLA class I ligands defined as the donor expressing a KIR gene for which the corresponding HLA class I ligand is not expressed by the recipient; KIR genotyping and HLA class I typing will be performed in the University of Wisconsin HLA laboratory; if all potential donors show the same degree of KIR/KIR-ligand mismatch, donors will be preferentially selected based on B haplotype KIR gene content DONOR: Genotypically haploidentical as determined by HLA typing\r\n* Preferably a non-maternal HLA haploidentical relative due to data of high incidence of graft failure with use of maternal HLA haploidentical cells\r\n* Eligible donors include biological parents, siblings or half-siblings, children, or cousins in rare instances Availability of at least one HLA- haploidentical (i.e. >= / and =< / HLA match) related donor (HLA-A, B, C, DR, and DQ loci) who is available to donate CD+ cells HLA identical (/) related donor available and readily accessible at time of transplantation evaluation DONOR: HLA-haploidentical first-degree relatives of the patient, including biological parents, siblings, or children, or half-siblings Patient must have available one or more potential first (biologic mother, sister, half-sister, or daughter) or second-degree related female donor; mothers and daughters have a % chance of being haploidentical matches, sisters a % chance of being matched or haploidentical, and second degree relatives have a % chance of being haploidentical matches; the donor and recipient must be HLA identical for at least one antigen at HLA-A, -B, -C and HLA-DRB Patients and selected donor must be HLA typed at high resolution using deoxyribonucleic acid (DNA) based typing at the following HLA-loci: HLA-A, -B, -C and DRB; donors must be HLA-haploidentical relatives including, but not limited to, children, siblings, or parents, defined as having a shared HLA haplotype between donor and patient at HLA-A, -B, -C, and -DRB DONOR: Partially HLA-mismatched relative (allele level matched at to of HLA loci: -A, -B, -C, and -DRB) DONOR: \r\n* HLA haploidentical relative of the patient; a unidirectional mismatch in either the graft versus host or host versus graft direction is considered a mismatch; the donor and recipient must be identical at least one allele (high resolution DNA-based typing) at the following genetic loci: HLA-A, -B, -C, and DRB \r\n* If patient over age years, may use HLA identical sibling donor\r\n* If patient has inherited bone marrow failure syndrome (IBMFS) and clear evidence of same disorder in potential related donors, unrelated donor may be used; unrelated donor must be a / match using HLA-A, -B, -C, DRB, and DPB; unrelated donor may also be used in case of donor specific antibodies to related donors or other clinical causes of unsuitable related donors Presence of anti-donor HLA antibodies (positive anti-donor HLA antibody is defined as a positive cross-match test of any titer by complement-dependent cytotoxicity or flow cytometric testing or the presence of anti-donor HLA antibody to the high expression loci HLA-A, B, C, or DRB with mean fluorescence intensity [MFI] > by solid phase immunoassay) DONOR: HLA-haploidentical donor/recipient match by molecular typing at the HLA-A, HLA-B and HLA-DRB loci DONOR: Recipient derived anti-donor HLA antibodies identified as unacceptable\ by Luminex assay; exceptions may be made by the Director of the Histocompatibility Laboratory in conjunction with the recipients physician and a plan for desensitization DONOR: Donor is blood-related and HLA-haploidentical to the recipient Patients must have a related donor who is human leukocyte antigen (HLA) mismatched at , , or antigens at the HLA-A; B; C; DR loci in the graft-versus-host disease (GVHD) direction; (patients with related donors who are HLA identical or are a -antigen mismatch may be treated on this therapeutic approach, but will have their outcomes will not be part of the statistical aims of the study); the HLA matched related category includes patients with a syngeneic donor DONOR: In addition to HLA determination, KIR genotyping will be performed on potential donors; preference will be given to donors who demonstrate KIR incompatibility with recipient HLA class I ligands defined as the donor expressing a KIR gene for which the corresponding HLA class I ligand is not expressed by the recipient; KIR genotyping and HLA class I typing will be performed in the University of Wisconsin HLA laboratory; the following KIR genes and corresponding HLA class I ligands will be analyzed:\r\n* KIR Gene; HLA Class I Ligand\r\n* KIRDLI; HLA Bw\r\n* KIRDL; HLA C^LYS\r\n* KIRDL/; HLA C^ASN\r\nIf all potential donors show the same degree of KIR/KIR-ligand mismatch, donors will be preferentially selected based on B haplotype KIR gene content according to the method described by Cooley et al., using the donor KIR B-content group calculator The recipient must have a related donor genotypically human leukocyte antigen (HLA)-A, B,C and DRB loci haploidentical to the recipient DONOR: Genotypically haploidentical as determined by HLA typing, preferably a non-maternal HLA haploidentical relative; eligible donors include biological parents, siblings or half siblings, or children DONOR: Donor with full haplotype HLA-mismatch will be preferred ( out of HLA match) to maximize graft-versus-leukemia (GVL) DONOR: HLA typing per University of Alabama (UAB) standard There are CMVpp-specific T-cells available in appropriate doses in the MSKCC Adoptive Immune T-cell Therapy Bank that are matched with the patient for HLA allele and that exhibit CMVpp-specific cytotoxic activity that is restricted by an HLA allele shared by the patient DONOR: HLA matching criteria DONOR: / HLA identical family donor HAPLOIDENTICAL RELATED DONOR: A haploidentical donor is a related donor that shares one haplotype in common with the recipient such that HLA compatibility will be a minimum of out of HLA loci matched; the HLA loci to be tested will be HLA A, B, Cw, DRB, and DQB; a minimum number of mismatches is desirable; however if several options are available the selection of a donor will be based on the loci where the mismatch occurs and the relative importance of its potential immunological function; donor-recipient pairs will initially be typed molecularly to provide a low resolution typing (antigen-level) to aid in the selection of the potential donor; upon review of the familial inheritance pattern, a qualified HLA staff member will review haplotype inheritance; high resolution (allele level) typing will be performed; final selection of a donor will be in consultation with National Cancer Institute (NCI) physicians and qualified HLA personnel; haploidentical related donors for pediatric recipients must be years of age or older; if more than one haploidentical related donor is available, we will evaluate each donor individually according to overall health, ABO matching, cytomegalovirus (CMV), etc. to select the donor Presence of a suitable first-degree related, human leukocyte antigen (HLA)-haploidentical or HLA-matched bone marrow donor\r\n* The donor and recipient must be identical at least one allele of each of the following genetic loci: HLA-A, HLA-B, HLA-Cw, HLA-DRB, and HLA-DQB; a minimum match of / is therefore required, and will be considered sufficient evidence that the donor and recipient share one HLA haplotype DONOR: Lack of recipient anti-donor HLA antibody; Note: in some instances, low level, non-cytotoxic HLA specific antibodies may be permissible if they are found to be at a level well below that detectable by flow cytometry; this will be decided on a case-by-case basis by the principal investigator (PI) and one of the immunogenetics directors DONOR: Donor must be a human leukocyte antigen (HLA)-haploidentical relative selected for best NK alloreactivity, defined as having a KIR gene present on the donor NK cells for which the relevant HLA haplotype (KIR ligand) is absent in the recipient and present in the donor or selected on the basis of activating KIR gene content Positive patient anti-donor HLA antibody, which is deemed clinically significant. Patients with acquired immunodeficiency syndrome (AIDS) developing EBV lymphomas or lymphoproliferative diseases as a consequence of the profound acquired immunodeficiency induced by human immunodeficiency virus (HIV); for such patients, EBV specific T-cells from third party seropositive donors who are HLA compatible in ) at least HLA antigens and ) one restricted allele shared by the patient will be used; selection of T cells known to be restricted by an HLA allele shared by the patient will be given priority Absence of a suitable partially HLA-mismatched (haploidentical), first-degree related donor; Note: determination of matching is based on allele or allele group level typing; to be considered haploidentical, the donor and recipient must be identical at least one allele of each of the following genetic loci: HLA-A, -B, -Cw, -DRB, and DQB; a minimum match of / is therefore required, and will be considered sufficient evidence that the donor recipient share one HLA haplotype; donors who are homozygous for the CCRdelta polymorphism are given preference DONOR: Donor must not be HLA identical to the recipient DONOR: Lack of recipient anti-donor HLA antibody; Note: in some instances, low level, non-cytotoxic HLA specific antibodies may be permissible if they are found to be at a level well below that detectable by flow cytometry; this will be decided on a case-by-case basis by the PI and one of the immunogenetics directors; pheresis to reduce anti-HLA antibodies is permissible; however eligibility to proceed with the transplant regimen would be contingent upon the result HAPLOIDENTICAL RELATED DONOR: A haploidentical donor that shares one haplotype in common with the recipient such that HLA compatibility will be a minimum of out of HLA loci matched; the HLA loci to be tested will be HLA A, B, Cw, DRB, and DQB; a minimum number of mismatches is desirable; however if several options are available the selection of a donor will be based on the loci where the mismatch occurs and the relative importance of its potential immunological function; donor-recipient pairs will initially be typed molecularly to provide a low resolution typing (antigen-level) to aid in the selection of the potential donor; upon review of the familial inheritance pattern, a qualified HLA staff member will review haplotype inheritance; high resolution (allele-level) typing will be performed; final selection of a donor will be in consultation with National Cancer Institute (NCI) physicians and qualified HLA personnel; if more than one haploidentical related donor is available, we will evaluate each donor individually according to overall health, ABO matching, cytomegalovirus (CMV), etc. to select the donor - INCLUSION CRITERIA:\n\n - Recipient:\n\n - Patients diagnosed with one of the following hematologic diseases which are\n associated with reasonable longevity, shown to be curable by allogeneic BMT but\n where concern for a high procedural mortality with conventional BMT may delay or\n prevent such treatment:\n\n - ) Paroxysmal nocturnal hemoglobinuria (PNH) associated with\n life-threatening thrombosis, and/or cytopenia, and/or transfusion dependence\n and/or recurrent and debilitating hemolytic crisis\n\n - ) Severe aplastic anemia (SAA) or pure red cell aplasia (PRCA [acquired or\n congenital]) associated with transfusion dependence and/or neutropenia in\n patients who are not candidates for, or who have failed immunosuppressive\n therapy\n\n - ) Refractory anemia (RA) or RARS MDS patients who have associated\n transfusion dependence and/or neutropenia.\n\n - Ages to (both inclusive), and weight >kg\n\n - Availability of HLA identical or single HLA locus mismatched family donor or\n / matched unrelated donor at the allelic level (HLA alleles A, B, C, DR, and\n DQ).\n\n - / donors where all the HLA sequences have the same antigen/peptide binding\n domains in key exons to the patient. This can result in identical protein\n sequences between patient and donor. Allele mismatches in p and g groups can be\n considered acceptable due to the exact matching which exists in the binding\n domains.\n\n - Telomere Length Testing\n\n - Germline/Inherited gene panel in patients where a suspicion for a familial bone\n marrow failure syndrome (BMFS) exists, TERC and TERT mutations testing will be\n performed on protocol -H- or performed elsewhere prior to enrolling on\n -H-.\n\n EXCLUSION CRITERIA:\n\n -Recipient: any of the following\n\n - Major anticipated illness or organ failure incompatible with survival from PBSC\n transplant\n\n - Diffusion capacity of carbon monoxide (DLCO) <% predicted (patients under the age of\n may be excluded from this criterion if they have difficulty performing the test\n correctly and thus are unable to have their DLCO assessed) using DL Adj and DL/VA/Adj.\n\n - Left ventricular ejection fraction <% (evaluated by ECHO) or <% (evaluated by\n MUGA)\n\n - Serum creatinine greater than .mg/dl or creatinine clearance less than ml/min by\n hr urine collection\n\n - Serum bilirubin greater than mg/dl, transaminases greater than times the upper\n limit of normal\n\n - Pregnant or lactating\n\n - Fanconi s anemia\n\n - ECOG performance status of or more (See Bone & Marrow Transplant Consortium\n Supportive Care Guidelines for HSCT Recipients)\n\n - Other malignant diseases liable to relapse or progress within years, with the\n exception of a separate hematologic malignancy where allogeneic stem cell transplant\n has been shown to be potentially curative.\n\n - Presence of an active infection not adequately responding to appropriate therapy.\n\n - Inability to comprehend the investigational nature of the study and provide informed\n consent. The procedure will be explained to subjects age - years with formal\n consent being obtained from parents or legal guardian.\n\n INCLUSION CRITERIA:\n\n -Related Donor:\n\n - HLA identical or single HLA mismatched family donor\n\n - Age greater than or equal to and less than or equal to years old\n\n - Weight > kg\n\n - If there is a suspicion of familial BMFS in the recipient, then the donor must have\n underong genetic testing for genes associated with BMFS -performed at a CLIA-certified\n laboratory, prior to enrolling in this protocol.\n\n EXCLUSION CRITERIA:\n\n -Related Donor: any of the following\n\n - Pregnant or lactating\n\n - Unfit to receive filgrastim (G-CSF) or undergo apheresis (history of stroke, MI,\n unstable angina, uncontrolled hypertension, severe heart disease or palpable spleen)\n\n - HIV positive (donors who are positive for HBV, HCV or HTLV-I/II, T.cruzi [Chagas] may\n be used at the discretion of the investigator following counseling and approval from\n the recipient)\n\n - Sickling hemoglobinopathies including HbSS or HbSC. Donors with HbAS are acceptable\n\n - Inability of donor or guardian of donor to comprehend the investigational nature of\n the study and provide informed consent.\n\n - Screening test positive for Chagas disease (Trypanosoma cruzi /T.\n cruzi/trypanosomiasis) confirmed by the Center for Disease Control (CDC).\n\n INCLUSION CRITERIA & EXCLUSION CRITERIA: Unrelated Donor\n\n -The NMDP unrelated donor inclusion criteria will be used as outlined in document (link).\n Donor eligibility will be completed per NMDP standards and in accordance with most recent\n and stringent FDA guidelines. DONOR: Related donors who are genotypically identical for one HLA haplotype and who may be mismatched at the HLA-A, -B, -C or DRB loci of the unshared haplotype with the exception of single HLA-A, -B or -C allele mismatches Have a related or unrelated human lymphocyte antigen (HLA) -identical donor or one antigen/allele mismatched in HLA-A, B, C or DRB DONOR: When more than one HLA-haploidentical donor is available, the donor with the lowest number of HLA allele mismatches will be chosen, unless there is HLA cross-match incompatibility, in which case donor selection is the responsibility of the project investigator (PI), in consultation with the immunogenetics laboratory; in cases where there is more than one donor with the least degree of mismatch, donors will be selected based on the most favorable combination of (i) HLA compatibility in cross-match testing and (ii) ABO compatibility: Available HLA-genotypically identical related donor No existing HLA-identical related donor is available Inclusion Criteria:\n\n . Signed informed consent\n\n . Patients with one of the life-threatening hematological malignancies:\n\n - Acute lymphocytic leukemia (ALL) in CR with high-risk features including adverse\n cytogenetics such as t(;), t(;), t(;), or MLL gene rearrangements;\n greater than cycle to achiever remission or with persistent MRD; ALL in second\n or greater remission with or without MRD. Acute myeloid leukemia (AML) in CR\n with high-risk features defined as: Greater than cycle of induction therapy\n required to achieve remission; Preceding myelodysplastic syndrome (MDS) or\n myeloproliferative disease; Presence of FLT mutations or internal tandem\n duplications; FAB M or M classification; Adverse cytogenetics, -, del q, -,\n delq, abnormalities involving q, q, q, q, q, , + [> abnormalities];\n\n - AML in second or greater remission, primary induction failure and patients with\n relapsed disease;\n\n - Advanced chronic myeloid leukemia (CML) who have progressed to blast phase or\n accelerated phase and are in need of a transplant and do not have an HLA matched\n donor;\n\n - MDS with IPSS intermediate- or higher or therapy-related MDS.Hodgkin lymphoma or\n Non-Hodgkin lymphoma (NHL): relapsed disease where remission duration is less\n than year, relapse after previous autologous transplant, or failure to achieve\n CR with chemotherapy.\n\n . Age ? years and ? years\n\n . Deemed eligible for allogeneic stem cell transplantation\n\n . Lack of suitable conventional donor (i.e. / related or unrelated donor) or presence\n of rapidly progressive disease not permitting time to identify an unrelated donor\n\n . HLA typing will be performed at high resolution (allele level) for the HLA-A, -B, Cw,\n and DRBl loci\n\n - A minimum genotypic identical haplotype match of / is required\n\n - The donor and recipient must be identical, as determined by high resolution\n typing, at least one allele of each of the following genetic loci: HLA-A, HLA-B,\n HLA-Cw, and HLA- DRB\n\n . Subjects with adequate organs function as measured by:\n\n - Cardiac: Left ventricular ejection fraction at rest must be >%\n\n - Pulmonary: FEV , FVC, DLCO (diffusion capacity) > % predicted (corrected for\n hemoglobin); or O saturation > % on room air\n\n - Hepatic: Direct bilirubin ? x upper limit of normal (ULN), or AST/ALT ? x ULN\n\n - Renal: Serum creatinine within normal range for age or creatinine clearance, or\n with a recommended GFR ? mL/min/.m\n\n . Performance status: Karnofsky ? %\n\n Exclusion Criteria:\n\n Subjects meeting the following criteria are NOT eligible for the study:\n\n . HLA / allele matched (HLA-A,-B,-Cw,-DRBl) related or unrelated donor able to donate;\n\n . Autologous hematopoietic stem cell transplant ? months prior to enrollment;\n\n . Prior allogeneic transplantation;\n\n . Active CNS involvement by malignant cells (less than months from the conditioning);\n\n . Current uncontrolled bacterial, viral or fungal infection (currently taking medication\n with evidence of progression of clinical symptoms or radiologic findings); the PI is\n the final arbiter of this criterion;\n\n . Positive HIV serology or viral RNA (? Grade III per CTCAE criteria);\n\n . Pregnancy (positive serum or urine ?HCG test) or breast-feeding;\n\n . Fertile men or women unwilling to use effective forms of birth control or abstinence\n for a year after transplantation;\n\n . Bovine product allergy.\n\n . Severe obesity (patient's weight is >/= .x the donor weight). DONOR: Institutional guidelines for HLA-match may be followed as long as the minimum criteria for HLA-matching as above are met Match-specific criteria:\r\n* HLA mismatched or haploidentical related donors: The donor and recipient must be haploidentical at a minimum of one allele of each of the following genetic loci: HLA-A, HLA-B, HLA-Cw, HLA-DRB, and HLA-DQB\r\n* Donor-specific anti-HLA antibody testing requirement: Testing for antibodies targeting donor specific HLA antigens at HLA-A, B, C, DRB, DQ and DP will be completed as per institutional standards\r\n* When more than one donor is available, the donor with the lowest number of HLA allele mismatches will be chosen, unless there is an HLA cross-match incompatibility or a medical reason to select otherwise, in which case donor selection is the responsibility of the principal investigator (PI); in cases where there is more than one donor with the least degree of mismatch, donors will be selected based on the most favorable combination of the factors below Myelodysplastic syndrome (MDS) with < % blasts by morphology and meets at least one of the following:\r\n* Received intensive induction chemotherapy (i.e. + or mitoxantrone, etoposide, and cytarabine [MEC]) OR\r\n* Progression after cycles of hypomethylating agents \r\n** The donor and recipient must be human leukocyte antigen (HLA) identical for at least one haplotype (using high resolution deoxyribonucleic acid [DNA] based typing) at the following genetic loci: HLA-A, HLA-B, HLA-C, and HLA-DRB DONORS: HLA-haploidentical related donor (aged to years) where donor and recipient must be HLA identical for at least one haplotype (using high resolution DNA based typing) at the following genetic loci: HLA-A, HLA-B, HLA-C, and HLA-DRB The unrelated UCB donors must be -/ human leukocyte antigen (HLA)-A, B, DRB matched with the recipient (HLA matching using molecular techniques: A and B at antigen level and DRB at allele level) and the UCB units must come from (a) qualified UCB bank(s) according to institutional standard operating procedures (SOPs); if the UCB unit is \unlicensed\ (most commonly on the basis of location [e.g., European countries], testing by non-Clinical Laboratory Improvements Amendment (CLIA) approved laboratories, or the UCB was collected before May , ), the Sponsor will make the final decision on patient eligibility based on the reason why the UCB is unlicensed\r\n* The patient must be free of HLA-specific antibodies for HLA antigens present on matched grafts\r\n* Suitable UCB units or haplo-identical donor available according to the UCB graft selection algorithm DONOR: Appropriate HLA-match to patient Patients must have a first-degree related donor or half-sibling who is at minimum HLA haploidentical to be enrolled; the donor and recipient must be identical at least one allele of each of the following genetic loci: HLA-A, HLA-B, HLA-Cw, HLA-DRB, and HLA-DQB; a minimum match of / is therefore required, and will be considered sufficient evidence that the donor and recipient share one HLA haplotype Positive leukocytotoxic crossmatch; specifically, complement dependent cytotoxicity and flow cytometric crossmatch assays must be negative, and the mean (or median) fluorescence intensity (MFI) of any anti-donor HLA antibody by solid phase immunoassay should be < ; if a screening assay against pooled HLA antigens is used, positive results must be followed with specificity testing using a single antigen assay; the MFI must be < unless the laboratory has validated higher threshold values for reactivity for HLA antigens, such as HLA-C, DQ, and DP, that may be enhanced in concentration on the single antigen assays; consult with principal investigator (PI) for the clinical significance of any anti-donor antibody Lack of suitable conventional donor (HLA identical sibling or HLA phenotypically identical relative or / unrelated donor evaluated using high resolution molecular typing) or presence of rapidly progressive disease not permitting time to identify an unrelated donor DONOR: Donor is blood-related and HLA-haploidentical to the recipient Have / allele-level, related or unrelated, medically cleared HSC donor matching at human leukocyte antigen (HLA)-A, HLA-B, HLA-C, and DRB- Presence of a suitable related, HLA-haploidentical or HLA-matched stem cell donor\r\n* The donor and recipient must be identical at least one allele of each of the following genetic loci: HLA-A, HLA-B, HLA-Cw, HLA-DRB, and HLA-DQB; a minimum match of / is therefore required for related donors, and will be considered sufficient evidence that the donor and recipient share one HLA haplotype Donors must be either:\r\n* HLA-haploidentical or HLA-identical relatives of the patient based on allele or allele group level typing Lack of recipient anti-donor HLA antibody\r\n* Note: in some instances, low level, non-cytotoxic HLA specific antibodies may be permissible if they are found to be at a level well below that detectable by flow cytometry; this will be decided on a case-by-case basis by the principal investigator (PI) and one of the immunogenetics directors; pheresis to reduce anti-HLA antibodies is permissible; however eligibility to proceed with the transplant regimen would be contingent upon the success of the desensitization DONOR: Haploidentical st-degree relative as defined by / or / HLA-matched at HLA -A, -B, or DRB who is - years of age Class I or II antibodies against donor HLA antigens HLA-Mismatched Related and Unrelated Donors: Patients who do not have an HLA-matched donor but have a related or unrelated donor who have one antigen or one allele mismatch at the HLA A, B, C, DRB or DQB loci; or who have two mismatches, at HLA-DQB and at one other locus will be eligible for entry on this protocol DONOR: Recipient derived anti-donor high-titer (> MFI) HLA antibody as determined by Luminex assay HAPLO-IDENTICAL DONOR: A HLA-haplo-identical related donor will be selected as available as per standard MSKCC adult bone marrow transplantation (BMT) guidelines; mismatched family members who are matched at more than of HLA-loci are permitted; factors to be taken into account when selecting a haplo-identical donor will include donor age, weight, health status and comorbidities, compliance, venous access, recipient donor specific HLA-antibody status, and natural killer (NK) cell alloreactivity The patient has an available NK cell donor who is a HLA haploidentical first-degree (parent, child, or sibling) or second-degree (child of a sibling) relative; minimum testing will be for HLA-A, HLA-B, and HLA-DR with donors matched for /, / or / antigens Donor/Recipient HLA Matching: HLA-mismatched related and unrelated donors: \r\n* Patients who do not have an HLA-matched donor but have a related or unrelated donor who have one antigen or one allele mismatch at the HLA A, B, C, DRB or DQB loci; or who have two mismatches, at HLA-DQB and at one other locus, will be eligible for entry on this protocol DONOR: Related, HLA-haploidentical donors who are identical for one HLA haplotype and mismatched for any number of HLA-A, -B, -C, DRB or DQB loci of the unshared haplotype Patients must have a related donor who is identical for one human leukocyte antigen (HLA) haplotype and mismatched at the HLA-A, -B or class II, DR beta (DRB) loci of the unshared haplotype with the exception of single HLA-A, -B or DRB mismatches DONOR: Related donor who is identical for one HLA haplotype and mismatched at the HLA-A, -B, or DRB loci of the unshared haplotype with the exception of single HLA-A, -B, or DRB mismatches RELATED DONORS: When more than one potential donor exists, priority should be given to donors based on HLA identity > cytomegalovirus (CMV) seronegativity > ABO compatibility > sex matching\r\n* Donor who is HLA phenotypically or genotypically identical at the allele level at HLA-A, -B, -C, -DRB, and -DQB\r\n* Must consent to G-CSF administration and leukapheresis; \r\n* Must have adequate veins for leukapheresis or agree to placement of central venous catheter (femoral, subclavian);\r\n* Only G-CSF mobilized PBMC only will be permitted as a hematopoietic stem cell (HSC) source on this protocol DONOR: HLA genotypically or phenotypically identical related donor Available human leukocyte antigen (HLA)-matched or -haploidentical, living related donor who is willing to donate bone marrow and part of liver; the donor and recipient must be HLA identical for at least one allele (using high resolution deoxyribonucleic acid [DNA] based typing) at the following genetic loci: HLA-A, HLA-B, HLA-C and HLA-DRB; fulfillment of this criterion shall be considered sufficient evidence that the donor and recipient share one HLA haplotype No donor-specific antibodies (DSA) using solid phase micro particle technology (by Luminex phenotype panel or Luminex single antigen bead test) performed days or less prior to transplant; as assessed by local laboratories; a positive anti-donor HLA antibody test is defined as the presence of an antibody against any one of the high expression HLA molecules (HLA-A, -B, -C, or DRB) with a mean fluorescence intensity (MFI) > by solid phase immunoassay Negative T and B cell flow crossmatches with the designated donor; as assessed by local laboratories; if one or more of the crossmatches is positive, the participant will be considered a screen failure unless combined results of antibody and cross match testing implicate a non-HLA antibody as the cause of the positive flow crossmatch; in this case, the protocol chair must approve the participant as a screening success after consultation with the HLA laboratory director Anti-donor HLA antibody using solid phase micro particle technology (by Luminex phenotype panel or Luminex single antigen bead test) performed days or less prior to transplant as assessed by local laboratories; the director of the immunogenetics laboratory will be responsible for determining what level of antibody is considered a positive anti-donor HLA antibody result DONOR: In case there are two or more donors with an equivalent HLA mismatch in the host-versus-graft (HVG) direction, donors will next be selected based on the most favorable combination of (i) HLA compatibility in cross-match testing and (ii) ABO compatibility:\r\n* HLA cross matching (in order of priority)\r\n. Mutually compatible (no cross-matching antibodies)\r\n. Recipient non-cross-reactive with donor, donor cross-reactive with recipient\r\n. Mutually cross-reactive\r\n* ABO compatibility (in order of priority)\r\n. Compatible\r\n. Minor incompatibility\r\n. Major incompatibility\r\n. Major and minor incompatibility DONOR: HLA-haploidentical donor/recipient match; if time permits and multiple donors are available, preference will be given to the KIR ligand mismatched donor (as predicted by HLA typing) Has a confirmed suitable HLA haploidentical donor available Recipient of a first renal allograft from a human leukocyte antigen (HLA)-haploidentical, living related donor; the donor and recipient must be HLA identical for at least one allele (using high resolution deoxyribonucleic acid [DNA] based typing) at the following genetic loci: HLA-A, HLA-B, HLA-C, and HLA-DRB; fulfillment of this criterion shall be considered sufficient evidence that the donor and recipient share one HLA haplotype DONOR: HLA-haploidentical, first-degree relatives or half-siblings of the recipient participant at the allele or allele group; the donor and recipient must be HLA identical for at least one allele (using high resolution DNA based typing) at the following genetic loci: HLA-A, HLA-B, HLA-C and HLA-DRB; fulfillment of this criterion shall be considered sufficient evidence that the donor and recipient share one HLA haplotype Presence of a suitable first-degree related, HLA-haploidentical or HLA-matched bone marrow donor;\r\n* The donor and recipient must be identical at least one allele of each of the following genetic loci: HLA-A, HLA-B, HLA-Cw, HLA-DRB, and HLA-DQB; a minimum match of / is therefore required, and will be considered sufficient evidence that the donor and recipient share one HLA haplotype DONOR: Donors must be HLA-haploidentical or HLA-identical, first-degree relatives of the patient based on allele or allele group level typing; half-siblings are not permitted DONOR; Lack of recipient anti-donor HLA antibody\r\n* Note: In some instances, low level, non-cytotoxic HLA specific antibodies may be permissible if they are found to be at a level well below that detectable by flow cytometry; this will be decided on a case-by-case basis by the PI and one of the immunogenetics directors; pheresis to reduce anti-HLA antibodies is permissible; however eligibility to proceed with the transplant regimen would be contingent upon the success of the desensitization Positive patient anti-donor lymphocyte crossmatch in HLA-A or B mismatched transplants; the definition of match is in Section ..; the crossmatch would only apply to mismatches at HLA-A or B, not DRB or HLA-C Related donor of T cells must be at least partially human leukocyte antigen (HLA) compatible, matching with recipient in at least / HLA loci (HLA-A, HLA-B, and HLA-DRB loci will be considered for this)\r\n* Donor selection priority: The original donor will be the first choice as source of T cells; If the original donor is unavailable for donation of peripheral mononuclear cells or does not meet all donor eligibility criteria, alternative related donors will be selected, with preference for those who have full HLA matching in / loci over those with partial HLA matching (>= / HLA loci) Presence of a suitable related, HLA?haploidentical or HLA?matched stem cell donor or unrelated matched donor\r\n* The donor and recipient must be identical at least one allele of each of the following genetic loci: HLA?A, HLA?B, HLA?Cw, HLA?DRB, and HLA?DQB; a minimum match of / is therefore required for related donors, and will be considered sufficient evidence that the donor and recipient share one HLA haplotype; unrelated donors will be / DONOR: donors must be either:\r\n* HLA?haploidentical or HLA?identical relatives of the patient based on allele or allele group level typing\r\n* Unrelated donor who is a / match to the recipient DONOR: lack of recipient anti?donor HLA antibody\r\n* Note: in some instances, low level, non?cytotoxic HLA specific antibodies may be permissible if they are found to be at a level well below that detectable by flow cytometry; this will be decided on a case?by?case basis by the principal investigator (PI) and one of the immunogenetics directors; pheresis to reduce anti?HLA antibodies is permissible; however eligibility to proceed with the transplant regimen would be contingent upon the success of the desensitization Presence of antibodies to a mismatched donor HLA antigen Absence of donor-specific antibodies (DSA) to the mismatched HLA-locus If a haploidentical donor is considered, parents, children, full siblings and in selected cases, extended family, will have high resolution typing at the MCC HLA laboratory; a familiar haploidentical donor is chosen among those who share at least one HLA-A, B, C, DRB and DQB haplotype with the patient Patient will be screened for antibodies targeting mismatched HLA antigens in potential haploidentical donors (donor specific antibodies, DSA); antibody screen and confirmatory testing using Luminex single antigen-bead test will be done Baseline positive donor-specific anti-HLA antibody testing Hematopoietic cell transplant (HCT)\r\n* No previous history of HCT or other cellular therapy (e.g., chimeric antigen receptor [CAR]-T cells, donor lymphocyte infusions)\r\n* Patient must be receiving cells from a first alternative donor defined as one of the following:\r\n** Unrelated donor with a complete human leukocyte antigen (HLA) match or a or HLA mismatch\r\n** Related donor with a or HLA mismatch Known presence of HLA antibodies against the non-shared donor haplotype Known presence of HLA antibodies against the non-shared donor haplotype Haploidentical family donor with to mismatches at the HLA-A, -B and/or -DR loci of the unshared haplotype