Ipilimumab After Allogeneic Stem Cell Transplant in Treating Patients With Persistent or Progressive Cancer

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