 The purpose of this phase II study is to assess the toxicity and efficacy of sequentially administered high dose chemotherapy followed by autologous stem cell rescue in the treatment of multiple myeloma. Prior studies have shown that dose-intensified melphalan can produce higher response rates and complete remission in some patients. Over the past several years, multiple phase II studies utilizing high dose chemotherapy or high dose chemo-radiotherapy with autologous marrow or peripheral blood stem cell rescue have demonstrated improved response rates and survival rates compared to historical controls. Recently a prospective randomized trial has demonstrated improved response rates, response duration and overall survival utilizing high dose therapy with autologous bone marrow support compared to standard chemotherapy. The primary cause of failure is relapse and it is unclear how many, if any, patients are cured by this approach. Based on observations of efficacy in Hodgkins Disease, Non-Hodgkins Lymphoma, and breast cancer, an approach utilizing sequential high dose chemotherapy in multiple myeloma was developed. This protocol tests the sequential regimen in multiple myeloma patients who have responded to a standard dose chemotherapy regimen prior to enrollment. 