Patients must be considered medically refractory to decreased immunosuppression (% or greater reduction) for at least week or there must be documentation in the medical chart that decreased immunosuppression would be associated with an unacceptable risk of rejection Has a medical condition that requires immunosuppression Evidence of clinically significant immunosuppression. Patients who receive sirolimus (Rapamune) as part of their transplant immunosuppression regimen Patients with chronic autoimmune disease(s) requiring systemic immunosuppression. Ongoing need for pharmacological immunosuppression, including steroids Use of corticosteroids or other immunosuppression (if patient had been taking steroids, at least weeks must have passed since the last dose) Receipt of any organ transplantation requiring ongoing immunosuppression Subjects with significant history of systemic immunosuppression due to drugs or infection with HIV or HTLV . Patients should not have an autoimmune disorder that requires active immunosuppression History of immunosuppression or autoimmunity, including human immunodeficiency virus (HIV), and organ or stem cell transplant, or an autoimmune condition previously treated with immunosuppressive therapy Immunosuppression, not related to prior treatment for malignancy. Patients receiving chronic steroids and or immunosuppression History of organ transplant requiring therapeutic immunosuppression Immunosuppression (human immunodeficiency virus [HIV] positive, heme/oxygenase [h/o] transplantation, lupus on immunosuppressive medication, etc.) The patient has a history of human immunodeficiency virus (HIV) or other known cause of immunosuppression, or is actively taking immunosuppressive medications due to organ transplantation, rheumatoid disease, or other medical conditions Received immunosuppression post hematopoietic transplant within month of study entry Chronic immunosuppression Immunosuppression (corticosteroids to prevent brain edema are permitted) Extensive chronic GvHD requiring ongoing immunosuppression with calcineurin inhibitors Patients with absolute lymphocyte count of < , who are known to be human immunodeficiency virus (HIV) positive, who have clinically significant active autoimmune disease, or are receiving immunosuppression following solid organ or stem cell transplant Significant immunosuppression. Immunosuppression: Any immunosuppressive medication must be stopped ? weeks prior to enrollment Significant immunosuppression from: Significant immunosuppression from: Evidence of clinically significant immunosuppression such as organ or stem cell transplantation, any severe congenital or acquired cellular and/or humoral immune deficiency, concurrent opportunistic infection. Significant immunosuppression from: No autoimmune disorder that requires active immunosuppression Absence of active GVHD and off immunosuppression; subjects on tapering prednisone will be eligible if their dose is . mg/kg or less and being actively tapered; we suggest a day waiting period off of immunosuppression but some subjects with rapidly progressive disease may need to be treated before days and will still be eligible Requirement for active immunosuppression to treat GVHD Current immunosuppression or taking immunosuppressive drugs Patients receiving a haploidentical / T cell-depleted transplant are eligible to follow a modified treatment plan that does not include withdrawal of immunosuppression Immunosuppression including primary, secondary, iatrogenic and idiopathic Patients with a diagnosis of chronic hepatitis B are ineligible due to the possibility of immunosuppression on study treatment Prior liver transplantation and on immunosuppression History of immune system abnormalities such as hyperimmunity (e.g., autoimmune diseases) that required systemic immunosuppression therapy and hypoimmunity (e.g., myelodysplastic disorders, marrow failures, acquired immunodeficiency syndrome (AIDS), ongoing pregnancy, transplant immunosuppression) Presence of systemic illness precluding definitive surgery or increasing the risk to patients due to potential immunosuppression. Ongoing immunosuppression with systemic steroids or other immune modulator Known immunosuppression (i.e. chronic steroid use) or autoimmune disorder Patients who require treatment with systemic corticosteroids for serious medical conditions or illnesses (e.g. immunosuppression after organ transplantation) Current immunosuppression (cancer, autoimmune disease) or taking immunosuppressive drugs History of organ transplant requiring therapeutic immunosuppression Known clinically significant autoimmune disorders requiring systemic immunosuppression for control Immunosuppression as a result of underlying illness or treatment; Patients on immunosuppression are also eligible Immunosuppression Has a diagnosis of an immunosuppressive illness or a condition requiring chronic immunosuppression Chronic immunosuppression Cyclosporine (CSP)-based postgrafting immunosuppression CSP-based postgrafting immunosuppression Patients who have chronic immunosuppression or are on current immunosuppressive therapies History or currently taking immunosuppression Evidence of clinically significant immunosuppression Evidence of clinically significant immunosuppression