Dasatinib for Modulating Immune System After Autologous Stem Cell Transplants for Multiple Myeloma, Non-Hodgkin, or Hodgkin Lymphoma

Inclusion Criteria: * Recipients of first ASCT for the treatment of hematologic malignancies (multiple myeloma, Hodgkin's and non Hodgkin's lymphoma) * Patients must be between 100 to 180 days after ASCT * Dasatinib use prior to ASCT is allowed * Performance status \>= 60% * Presence of LGL clone prior to enrollment will not be an exclusion criterion if the LGL clone is \< 25% of T cell population * Total bilirubin \< 2.0 times the institutional upper limit of normal (ULN) * Hepatic enzymes (aspartate aminotransferase \[AST\], alanine aminotransferase \[ALT\]) =\< 2.5 times the institutional ULN * Serum creatinine \< 1.5 times the institutional ULN * Hemoglobin \>= 8 g/dL * Absolute neutrophil counts \>= 1,500 cells per uL * Platelets \>= 100,000 per uL * Patient should be able to provide signed written informed consent; before any study procedures are performed, subjects will have the details of the study described to them, and they will be given a written informed consent document to read; then, if subjects consent to participate in the study, they will indicate that consent by signing and dating the informed consent document in the presence of study personnel; written consent will include a Health Insurance Portability and Accountability Act (HIPAA) form according to institutional guidelines * Patient should be able to take oral medication (dasatinib must be swallowed whole) Exclusion Criteria: * Patients who have evidence of disease progression before day 100 after ASC…