Using Fostamatinib to Treat Post-Hematopoietic Stem Cell Transplant Immune-mediated Cytopenias

* INCLUSION CRITERIA: * Ages 18-75 years inclusive * Ability to comprehend the investigational nature of the study and provide informed consent * Female patients of reproductive potential agree to avoid pregnancy through abstinence or the use two forms of highly effective birth control during and for 1 month after the last study treatment and agree not to donate eggs during this time * male patients of reproductive potential agree to avoid pregnancy of a partner through abstinence or the use two forms of highly effective birth control during and for 1 month after the last study treatment and agree not to donate sperm during this time. * Diagnosis of an immune mediated cytopenia (anemia and/or thrombocytopenia) in a patient that either: * Failed or relapsed after at least one line of therapy including steroids, IVIG, TPO mimetics, rituximab, azathioprine, cyclophosphamide, cyclosporine, tacrolimus, danazol, vincristine, ESA or splenectomy * Or remains transfusion dependent (\>=1 transfusion(s)/2 weeks) * Or is steroid dependent * Subjects are \>=60 days post-allogeneic transplant with: * Thrombocytopenia, defined as average platelets count \<30 x 10\^9/L for 3 consecutive available readings at least 2 weeks apart, after other cell lines have engrafted, with no counts \>40 x 10\^9/L unless from rescue transfusions. Subjects failed at least one line of therapy outlined above with a clinical diagnosis of immune mediated thrombocytopenia. * Anemia, transfusion dependent, or defined as hemoglobin \<=9 g/dL for 3 consecutive available readings at least 2 weeks apart, after other cell lines have engrafted OR if hemoglobin 9-10 g/dL, subject must have symptomatic anemia or ongoing treatment for immune hemolytic anemia that have failed at least one line of therapy outlined above. Symptomatic anemia is defined as anemia with fatigue, weakness, shortness of breath, palpitations/fast heartbeat, lightheadedness, and/or chest pain, and these symptoms are attributed to anemia. Laboratory evaluation are recommended but not required for the diagnosis, such as a positive DAT, low haptoglobin \<lower limit of normal (LLN), indirect bilirubin \> upper limit of normal (ULN), or lactate dehydrogenase (LDH) \>ULN. * Subjects must test negative for HIV, HBV, and HCV by standard serologic tests within the previous six months * Subjects on other standard of care therapeutic regimens for GVHD or cytopenias should be on a stable dose of medication (no change \>=25%) for at least 15 days prior to enrollment. * Patients with a history of hypertension should be maintained on a stable antihypertensive regimen and with controlled blood pressure (Systolic blood pressure \< 140 mmHg and diastolic blood pressure \<90 mmHg) for at least one week prior to enrollment. * Peripheral blood or bone marrow T-cell chimerism \>=50% donor cells * Immune mediated anemia in subjects with auto or alloantibodies identified due to ABO or non-ABO mismatch transplant, or thrombocytopenia due to identified HLA/HPA antibody. Other causes of immune mediated cytopenias include clinically diagnosed (with or without serologic confirmation) idiopathic thrombocytopenic purpura or autoimmune hemolytic anemia. Subjects with cytopenias attributable to GVHD will be included. Subjects with idiopathic immune mediated cytopenias can also be included. Subjects with evidence for graft rejection per the investigator's opinion ARE NOT eligible for treatment. Steroid dependence is defined as inability to tolerate a corticosteroid taper after demonstrating a response to an initial corticosteroid dose (typically 1-2 mg/kg/day). Patients will meet our definition of steroid dependence if their cytopenias relapse or progress before achieving a 50% decrease in the initial corticosteroid dose and/or are unable to have their steroid dose tapered to a dose of less than 20 mg/day of prednisone. EXCLUSION CRITERIA: * Severe psychiatric illness or mental deficiency sufficient to make making informed consent impossible * Positive pregnancy test for women of childbearing age within 1 week or being actively lactating * Immune mediated cytopenia responsive to the standard of care treatment * Immune mediated cytopenia due to other autoimmune causes, such as systemic lupus erythrocytosis, chronic lymphocytic leukemia * Patients who have previously received or currently take fostamatinib post-allogeneic transplant * Non-immune mediated cytopenias. Etiologies including, but not limited to, cytopenias due to HIV infection, lymphoproliferative disorders, myelodysplasia/acute leukemia, drug-induced thrombocytopenia, thrombotic microangiopathies, acute bleeding, consumptive coagulopathy, fever, infections leading to cytopenia, medications induced cytopenias, thrombotic microangiopathies (disseminated intravascular coagulation), splenomegaly or hemophagocytic lymphohistiophagocytosis, relapse of primary disease. * Patients with neutropenia, defined as absolute neutrophil count \<=1.0 x 10\^9/L, will be excluded * Uncontrolled hypertension (systolic blood pressure \>=140mmHg or diastolic blood pressure \>=90mmHg) * ALT or AST \>=3 times the upper limit of normal, or direct bilirubin \>=2 times the upper limit of normal * Patients who have a history of medical disorders, that in the investigator's opinion, could affect the conduct of the study or the absorption, metabolism or excretion of the study drug are excluded. * Patients with lymphoma/chronic lymphocytic leukemia, hepatitis, or HIV associated with ITP/wAIHA * Patients with evidence of graft rejection (based on clinical suspicion supported by BM biopsy data and/or chimerism studies and/or MLR) * Subjects recently treated (within 30 days) with cytokine-targeting biologics (anti-TNF, IL6) or Bcell or plasma-cell depleting antibody. * Other cancers except that for which the transplant was done \< 2 years before study entry, except non-melanoma skin cancer or carcinoma in situ of the uterine cervix or breast