Discontinuation or Continuation of Immunosuppressive Therapy in Participants With Chronic Graft Versus Host Disease

PRIMARY OBJECTIVE: I. Assess feasibility of enrolling and randomizing patients with chronic graft versus host disease (GVHD) to discontinuation (standard of care) versus continuation (investigation) of immunosuppressive therapy (IST). SECONDARY OBJECTIVES: I. Assess feasibility of enrolling and randomizing patients who are not local, and evaluate the quality of data received for those patients. II. Assess whether prolonged IST decreases the need for pulses of high dose IST. III. Evaluate the effect of prolonged IST on chronic GVHD manifestations and severity, risk of relapse, infection and organ toxicity. OUTLINE: Participants are randomized to 1 of 2 arms. ARM I: Participants have their IST tapered and discontinued per the plan. ARM II: Participants continue to receive a fixed dose IST for an additional 9 months with no taper. After completion of study treatment, participants are followed up annually.