Inclusion Criteria:

- Molecular based human leukocyte antigens (HLA) typing will be performed for the
HLA-A, -B, -Cw, -DRB1 and -DQB1 loci to the resolution adequate to establish
haplo-identity; a minimum match of 5/10 is required

- An unrelated donor search is not required for a patient to be eligible for this
protocol if the clinical situation dictates an urgent transplant; clinical urgency is
defined as 6-8 weeks from referral or low-likelihood of finding a matched, unrelated
donor

- Acute leukemias (includes T lymphoblastic lymphoma) in remission

- Remission is defined as < 5% blasts with no morphological characteristics of acute
leukemia (e.g., Auer Rods) in a bone marrow with > 20% cellularity, peripheral blood
counts showing ANC > 1000/ul, including patients in complete remission with
incomplete platelet recovery (CRp)

- Acute Lymphoblastic Leukemia in high risk first complete remission (CR1) as defined
by at least one of the following:

- Adverse cytogenetics such as t(9;22), t(1;19), t(4;11), mixed lineage leukemia
(MLL) rearrangements

- White blood cell counts > 30,000/mcL

- Patients over 30 years of age

- Time to complete remission > 4 weeks

- Presence of extramedullary disease

- Acute Myelogenous Leukemia in high risk CR1 as defined by at least one of the
following:

- Greater than 1 cycle of induction therapy required to achieve remission

- Preceding myelodysplastic syndrome (MDS)

- Presence of fms-like tyrosine kinase receptor-3 (Flt3) abnormalities; or
French-American-British (FAB) M6 or M7 leukemia

- OR adverse cytogenetics for overall survival such as:

- Those associated with MDS

- Complex karyotype (>= 3 abnormalities); or

- Any of the following: inv(3) or t(3;3), t(6;9), t(6;11), + 8 [alone or with
other abnormalities except for t(8;21), t(9;11), inv(16) or t(16;16)],
t(11;19)(q23;p13.1)

- Acute Leukemias in 2nd or subsequent remission

- Biphenotypic/Undifferentiated Leukemias in 1st or subsequent CR

- High-risk MDS status-post cytotoxic chemotherapy

- Burkitt's lymphoma: second or subsequent CR

- Chemotherapy-sensitive (complete or partial response) large cell, Mantle Cell or
Hodgkin's lymphomas that have failed at least 1 prior regimen of multi-agent
chemotherapy and are ineligible for an autologous transplant

- Marginal zone B-cell lymphoma or follicular lymphoma that has progressed after at
least two prior therapies (excluding single agent Rituxan)

- Multiple myeloma (MM) Stage II or III patients who have progressed after an initial
response to chemotherapy or autologous hematopoietic stem cell transplantation (HSCT)
or MM patients with refractory disease who may benefit from tandem
autologous-nonmyeloablative allogeneic transplant

- Left ventricular ejection fraction at rest must be >= 35%

- Bilirubin =< 2.5 mg/dL

- Alanine aminotransferase (ALT) < 5 x upper limit of normal (ULN)

- Aspartate aminotransferase (AST) < 5 x ULN

- Alkaline phosphatase < 5 x ULN

- Serum creatinine within normal range for age, or if serum creatinine outside normal
range for age, then renal function (creatinine clearance or glomerular filtration
rate [GFR]) > 40 mL/min/1.73m^2

- Forced expiratory volume in one second (FEV1), forced vital capacity (FVC), diffusion
capacity of carbon monoxide (DLCO) (diffusion capacity) >= 40% predicted (corrected
for hemoglobin); if unable to perform pulmonary function tests, then oxygen (O2)
saturation > 92% on room air

- Karnofsky/Lansky score >= 60%

- Patients who have received a prior allogeneic HSCT and who have either rejected their
grafts or who have become tolerant of their grafts with no active GVHD requiring
immunosuppressive therapy

- DONOR: Donors must be HLA-haploidentical first-degree relatives of the patient;
eligible donors include biological parents, siblings, or children, or half-siblings

- DONOR: Age >= 12 years

- DONOR: Weight >= 40 kg

- DONOR: Ability of donors < 18 years of age to undergo apheresis without use of a
vascular access device; vein check must be performed and verified by an apheresis
nurse prior to arrival at the Seattle Cancer Care Alliance (SCCA)

- DONOR: Donors must meet the selection criteria as defined by the Foundation for the
Accreditation of Cell Therapy (FACT) and will be screened per the American
Association of Blood Banks (AABB) guidelines

Exclusion Criteria:

- HLA-matched or single allele-mismatched donor able to donate

- Pregnancy or breast-feeding

- Current uncontrolled bacterial, viral or fungal infection (currently taking
medication with evidence of progression of clinical symptoms or radiologic findings)

- Patients with primary idiopathic myelofibrosis

- DONOR: Positive anti-donor HLA antibody