Inclusion Criteria:

- Diagnosis of persistent or progressive hematologic malignancy or solid tumor after
allogeneic hematopoietic stem cell transplantation (AHSCT)

- Patients are eligible for study entry at any time between post-transplantation day 90
and 3 years after withdrawal of immunosuppressive therapy

- Acute myeloid leukemia (AML) or acute lymphoblastic leukemia (ALL) that meets any of
the following criteria: hematologic relapse by standard criteria, hematologic
persistence evidenced by bone marrow blasts > 10% after day 30 post-AHSCT

- Cytogenetic progression as evidenced by an increase in the percentage of Philadelphia
chromosome (Ph)1-positive metaphases (or Ph1-positive cells by fluorescent in situ
hybridization) from complete cytogenetic response (0% Ph1-positive cells) to partial
response (1-34% Ph1-positive cells); PR to minor response (35-94% Ph1-positive
cells); or MR to no response (95-100% Ph1-positive cells)

- Resistance to imatinib mesylate, defined as disease progression (hematologic,
cytogenetic, or molecular) during OR failure to respond to (i.e., lack of complete
hematologic response after 3 months, lack of partial cytogenetic response after 6
months, or lack of complete cytogenetic response after 12 months) prior imatinib
mesylate therapy

- Myelodysplastic syndromes that meet any of the following criteria:

Hematologic relapse by standard criteria, cytogenetic relapse evidenced by recurrence of
clonal abnormality in patients who achieved CCR after AHSCT, hematologic persistence
evidenced by cytopenias not attributable to other post-transplant causes accompanied by
characteristic morphological changes more than 90 days after AHSCT

- OR; Hematologic persistence evidenced by cytopenias not attributable to other
post-transplant causes accompanied by characteristic morphological changes more than
90 days after AHSCT, or cytogenetic persistence evidenced by persistence of clonal
abnormality more than 90 days after AHSCT

- Chronic lymphocytic leukemia that meets any of the following criteria:

greater than 25% increase in absolute lymphocytosis of > 5,000/mm3, greater than 25%
increase in measurable lymphadenopathy, persistence of absolute lymphocytosis of >
5,000/mm3 at day 90 or later after AHSCT, persistence of lymphadenopathy of ≥ 3 cm in
diameter at day 90 or later after AHSCT

- Aggressive non-Hodgkin's lymphoma (e.g., diffuse large cell lymphoma, lymphoblastic
lymphoma, mantle cell lymphoma, or peripheral T cell lymphoma), Hodgkin's lymphoma,
OR solid tumor that meets any of the following criteria: greater than 50% increase in
measurable or evaluable disease, persistence of measurable lesions > 3.0 cm in
diameter at day 90 or later after AHSCT OR;

- Persistence of malignancy by biopsy or positron emission tomography scan unless there
is clear evidence of progression

- Multiple myeloma with demonstrated resistance to or intolerance of prior thalidomide
and bortezomib unless these agents are contraindicated (e.g., due to peripheral
neuropathy) and meeting any of the following criteria: greater than 25% increase in
paraprotein band, abnormal quantitative immunoglobulin level, or urine protein
excretion OR

- Greater than 25% increase in percent of plasma cells in the bone marrow (if > 15%),
presence of new lytic bone lesions, new extramedullary lesions OR ≥ 25% enlargement
of existing extramedullary lesions, persistence of paraprotein band, abnormally
elevated quantitative immunoglobulin level, or bone marrow plasmacytosis > 15% for a
period of at least 90 days after AHSCT

- At least 1 bidimensionally measurable lesion ≥ 1.5 cm in diameter

- Evaluable disease is defined as disease that is assessable for response (e.g.,
pleural effusion, elevated serum tumor)

- Bone metastases that can be assessed by CT scan or MRI considered evaluable

- Leukemia is considered evaluable disease

- Patients who met criteria for persistence or progression with AML, ALL, CML, or
aggressive NHL AND are currently in complete remission after reinduction therapy do
not require measurable or evaluable disease to be eligible

- At least 50% donor chimerism in the T-cell lineage OR full (≥ 90%) donor chimerism in
unseparated blood on last assessment within 3 months before study entry

- No evidence on consecutive testing of > 10% decline in T-cell chimerism beyond the
error of the test

- ECOG 0-2

- Life expectancy: More than 3 months

- No prior grade 3 or 4 acute graft-vs-host disease

- No concurrent autoimmune diseases requiring the chronic use of immunosuppressive
medications, active connective tissue disease, CNS disease including multiple
sclerosis or demyelinating disease, inflammatory bowel disease, autoimmune hepatitis

- No ongoing serious infection

- Negative pregnancy test

- Fertile patients must use effective contraception during and for at least 4 months
after study therapy

- No other serious ongoing medical condition that would preclude study participation

- No other malignancy within the past 5 years

- No psychological or psychiatric condition that would preclude study participation

- No prior anti-cytotoxic T-lymphocyte-associated antigen-4 monoclonal antibody
(MDX-010)

- At least 6 weeks since prior immunosuppressive agents

- At least 2 weeks since prior imatinib mesylate

- No concurrent imatinib mesylate

- At least 6 weeks since prior and no concurrent immunosuppressive agents for
clinically active graft-versus-host disease (GVHD) prophylaxis or treatment

- No other concurrent investigational agents

- OR Cytogenetic persistence evidenced by any Ph1-positive metaphases in bone marrow
after day 90 post-AHSCT