Patients for whom the best available donor is mismatched at both HLA class I and class II DONOR: If the patient is homozygous at the mismatch HLA class I locus or II locus, the donor must be heterozygous at that locus and one allele must match the patient (i.e., patient is homozygous A*01:01 and donor is heterozygous A*01:01, A*02:01); this mismatch will be considered a one-antigen mismatch for rejection only DONOR: Patients who are homozygous at the mismatched HLA class I locus or II locus, the donor is excluded if homozygous at the mismatched locus (i.e., patient is homozygous A*01:01 and donor is homozygous A*02:01); this type of mismatch is considered a two-antigen mismatch and is not allowed HLA-haploidentical related donor (aged 12 to 70 years) DONOR: Patients who are homozygous at the mismatched HLA class I or II locus, the donor is excluded if homozygous at the mismatched locus (i.e., patient is homozygous A *01:01 and donor is homozygous A *02:01); this type of mismatch is considered a two-antigen mismatch and is not allowed HLA-MISMATCHED UNRELATED DONOR: If the patient is homozygous at the mismatch HLA class I locus or II locus, the donor must be heterozygous at that locus and one allele must match the patient (i.e., patient is homozygous A*01:01 and donor is heterozygous A*01:01, A*02:01); this mismatch will be considered a one-antigen mismatch for rejection only Available HLA-matched or better but not fully HLA-matched (2/4 or 3/4 antigens) related donor (aged 18 to 75 years) with donor/recipient match based on a minimum of intermediate resolution deoxyribonucleic acid (DNA) based class I typing of the A and B locus who is cytomegalovirus (CMV) seropositive DONOR: Haploidentical by human leukocyte agent (HLA)-typing\r\n* Haploidentical family members, between the ages of 18 and 65 years, identified as an eligible donor by HLA-typing.; a biological parent will generally be used as the donor Available human leukocyte antigen (HLA)-matched or better but not fully HLA-matched (2/4 or 3/4 antigens) related donor (aged 18 to 75 years) with donor/recipient match based on a minimum of intermediate resolution deoxyribonucleic acid (DNA) based class I typing of the A and B locus who is CMV seropositive Human leukocyte antigen (HLA)-haploidentical related donor (aged 12 to 75 years) with donor/recipient match based on a minimum of intermediate resolution deoxyribonucleic acid (DNA) based class I typing of the A and B locus (at least 2/4 class I allele) HLA-haploidentical related donor (aged 12 to 75 years) with donor/recipient match based on a minimum of intermediate resolution DNA based class I typing of the A and B locus (at least 2/4 class I allele) Available HLA-haploidentical or mismatched related donor (aged 12 to 70 years) with donor/recipient match based on a minimum of intermediate resolution deoxyribonucleic acid (DNA) based class I typing of the A and B locus (at least 2/4 class I allele) DONOR: HLA-haploidentical or mismatched related donor/recipient match based on a minimum of intermediate resolution DNA based Class I typing of the A and B locus (at least 2/4 class I allele) DONOR: Donor is blood-related and HLA-haploidentical to the recipient Available human leukocyte antigen (HLA)-haploidentical donor that meets the following criteria:\r\n* Related donor (sibling, offspring, or offspring of sibling)\r\n* At least 18 years of age\r\n* HLA-haploidentical donor/recipient match by at least class I serologic typing at the A&B locus\r\n* In general good health, and medically able to tolerate leukapheresis required for harvesting the NK cells for this study\r\n* Negative for hepatitis, human T-cell lymphotropic virus (HTLV), and human immunodeficiency virus (HIV) on donor viral screen\r\n* Not pregnant\r\n* Voluntary written consent to participate in this study DONOR: Evaluation: history and physical examination; laboratory examinations: hematology, electrolytes, chemistry; infectious disease screening and serology; HLA typing; KIR typing will not be indicated if there is only one haploidentical donor; KIR typing is advised to be done if feasible and does not delay transplant Available related human leukocyte antigen (HLA)-haploidentical NK cell donor by at least class I serologic typing at the A&B locus DONOR: HLA-haploidentical donor/recipient match by at least class I serologic typing at the A&B locus Available related human leukocyte antigen (HLA)-haploidentical donor (aged 14 to 75 years) with donor/recipient match based on a minimum of intermediate resolution DNA based class I typing of the A&B locus DONOR: Donor/recipient match based on a minimum of intermediate resolution DNA based class I typing of the A&B locus DONOR: HLA-haploidentical donor/recipient match by at least class I serologic typing at the HLA-A and B loci DONOR: Donor is blood-related and HLA-haploidentical to the recipient Available related human leukocyte antigen (HLA)-haploidentical donor (aged 14-75 years) by at least class I serologic typing at the A & B locus DONOR: HLA-haploidentical donor/recipient match by at least class I serologic typing at the A & B locus Available related human leukocyte antigen (HLA)-haploidentical donor by at least class I serologic typing at the A&B locus DONOR: HLA-haploidentical donor/recipient match by at least class I serologic typing at the A&B locus Available related human leukocyte antigen (HLA) haploidentical NK cell donor by at least Class I serologic typing at the A and B locus (age 12-75 years) 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 Available human leukocyte antigen (HLA)-haploidentical donor that meets the following criteria:\r\n* Immediate family member (sibling, offspring, or parent)\r\n* HLA-haploidentical donor/recipient match by class I serologic typing at the A&B locus\r\n* In the treating physician’s opinion, is in general good health, and medically able to tolerate leukapheresis required for harvesting hematopoietic stem cells (HSC)\r\n* No active hepatitis (B, C), human T-cell lymphotropic virus (HTLV), and human immunodeficiency virus (HIV) infections\r\n* Not pregnant