Inclusion Criteria

DISEASE CHARACTERISTICS:

- Diagnosis of one of the following high-risk hematologic malignancies:

- Chronic myelogenous leukemia meeting one of the following criteria:

- Disease in chronic phase and resistant to available tyrosine kinase
inhibitors

- Disease in accelerated phase

- Disease with blast crisis that has entered into a second chronic phase
after induction chemotherapy

- Acute myelogenous leukemia meeting the following criteria:

- Marrow blasts < 5% but persistence of minimal residual disease by flow
cytometry, cytogenetics, or FISH

- Must meet one of the following criteria:

- Disease in second or subsequent complete remission

- Primary induction chemotherapy failure with disease subsequently
entering complete remission

- Disease in first complete remission with poor-risk cytogenetics or
arising from preceding hematological disease

- Myelodysplastic syndrome meeting at least one of the following criteria:

- Treatment-related

- Monosomy 7 or complex cytogenetics

- International prognostic scoring system score ≥ 1.5

- Chronic myelomonocytic leukemia

- Acute lymphocytic leukemia or lymphoblastic lymphoma meeting the following
criteria:

- Marrow blasts < 5% but persistence of minimal residual disease by flow
cytometry, cytogenetics, or FISH

- Must meet one of the following criteria:

- Disease in second or subsequent complete remission

- Acute lymphocytic leukemia with poor-risk karyotype [e.g., t(9;22) or
bcr-abl fusion, t(4;11), or other MLL translocation] and in first
complete remission

- Chronic lymphocytic leukemia or prolymphocytic leukemia meeting both of the
following criteria:

- Previously treated disease that has either relapsed or failed to respond
adequately to conventional-dose therapy including purine analogs

- In the opinion of the transplant physician, unlikely to benefit from
reduced intensity transplantation due to the presence of one or more
high-risk features (i.e., bulky tumor masses, B symptoms, and/or inadequate
response to salvage chemotherapy)

- Hodgkin or non-Hodgkin lymphoma (including low-grade, mantle cell, and
intermediate-grade/diffuse disease) meeting the following criteria:

- Previously treated disease that has either relapsed or failed to respond
adequately to conventional-dose therapy or autologous transplantation

- In the opinion of the transplant physician, unlikely to benefit from
reduced intensity transplantation due to the presence of one or more
high-risk features (i.e., bulky tumor masses, B symptoms, and/or inadequate
response to salvage chemotherapy) NOTE: A new classification scheme for
adult non-Hodgkin lymphoma has been adopted by PDQ. The terminology of
"indolent" or "aggressive" lymphoma will replace the former terminology of
"low", "intermediate", or "high" grade lymphoma. However, this protocol
uses the former terminology.

- No available matched related or unrelated donor OR a matched related or unrelated
donor will not be available in the time frame necessary to perform a transplant

- Availability of a first-degree relative (parent, child, sibling) matched at 3/6-5/6
loci (HLA-A, -B, -DR)

- Donor must be willing to donate mobilized peripheral blood stem cells

- No positive HLA crossmatch in the host-vs-graft direction or high titer
donor-specific antibodies

PATIENT CHARACTERISTICS:

- Karnofsky performance status 70-100%

- Bilirubin < 2 mg/dL (unless due to hemolysis, Gilbert syndrome, or primary
malignancy)

- Creatinine < 2 mg/dL OR creatinine clearance ≥ 40 mL/min

- Not pregnant

- Fertile patients must use effective contraception

- LVEF ≥ 45%

- FEV_1 and forced vital capacity ≥ 50% predicted

- No HIV positivity

- No debilitating medical or psychiatric illness that would preclude giving informed
consent or receiving optimal treatment and follow-up

PRIOR CONCURRENT THERAPY:

- See Disease Characteristics

- No immunosuppressive agents ≤ 24 hours after completion of post-transplant
cyclophosphamide (including steroids as antiemetics)