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

This study uses a drug called dasatinib to produce an anti-cancer effect called large granular lymphocyte cellular expansion. Large granular lymphocytes are blood cells known as natural killer cells that remove cancer cells. Researchers think that dasatinib may cause large granular lymphocyte expansion to happen in patients who have received a blood stem cell transplant (SCT) between 3 to 15 months after the blood SCT. In this research study, researchers want to find how well dasatinib can be tolerated, the best dose to take of dasatinib and to estimate how often large granular lymphocytic cellular expansion happens at the best dose of dasatinib.

This is a phase I, dose-escalation study.

Eligibility Criteria:
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 ASCT
* Sex and reproductive status:

  * Women of childbearing potential (WOCBP) who are unwilling or unable to use an acceptable method to avoid pregnancy for the entire study period and for at least 4 weeks after the last dose of study drug
  * Women who are pregnant or breastfeeding
  * Women with a positive pregnancy test
  * Sexually active fertile men not using effective birth control if their partners are WOCBP
* Medical history and concurrent diseases:
* No malignancy (other than the one treated in this study) which required radiotherapy or systemic treatment within the past 5 years
* Concurrent medical condition which may increase the risk of toxicity, including:

  * Pleural or pericardial effusion of any grade at the time of screening for study
  * Cardiac symptoms; any of the following should be considered for exclusion:

    * Uncontrolled angina, congestive heart failure or myocardial infarction (MI) (within 6 months)
    * Diagnosed congenital long QT syndrome
    * Any history of clinically significant ventricular arrhythmias (such as ventricular tachycardia, ventricular fibrillation, or torsades de pointes)
    * Prolonged corrected QT (QTc) interval on pre-entry electrocardiogram (\> 450 msec)
* History of significant bleeding disorder unrelated to cancer, including:

  * Diagnosed congenital bleeding disorders (e.g., von Willebrand's disease)\* Diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies)
  * Ongoing or recent (=\< 3 months) significant gastrointestinal bleeding
* Any previous history of \>= grade 3 toxicity to dasatinib
* Prohibited treatments and or therapies
* Category I drugs that are generally accepted to have a risk of causing torsades de pointes including: (patients must discontinue drug 7 days prior to starting dasatinib):

  * Quinidine, procainamide, disopyramide
  * Amiodarone, sotalol, ibutilide, dofetilide
  * Erythromycin, clarithromycin
  * Chlorpromazine, haloperidol, mesoridazine, thioridazine, pimozide
  * Cisapride, bepridil, droperidol, methadone, arsenic, chloroquine, domperidone, halofantrine, levomethadyl, pentamidine, sparfloxacin, lidoflazine
* Patient agrees to discontinue St. Johns Wort while receiving dasatinib therapy (discontinue St. Johns Wort at least 5 days before starting dasatinib)
* Patient agrees that intravenous (IV) bisphosphonates will be withheld for the first 8 weeks of dasatinib therapy due to risk of hypocalcemia
* Other exclusion criteria:
* Prisoners or subjects who are involuntarily incarcerated
* Subjects who are compulsorily detained for treatment of either a psychiatric or physical (eg, infectious disease) illness