Etanercept is a drug that blocks a chemical called Tumor Necrosis Factor (TNF) from causing damage to your tissue. The purpose of etanercept is to help improve the response to standard treatment for GVHD. Previous studies have shown that less than 50% of patients respond fully to GVHD treatment. Without a good response, patients often have a prolonged treatment for this disease, often involving hospitalization and sometimes even death. Etanercept (Enbrel) will be added to the standard treatment to see if we can lower the rate of GVHD and the risk of death from GVHD by blocking TNF.