Intensive chemotherapy is associated with significant thrombocytopenia, often requiring platelet transfusion to maintain platelet counts. This investigational drug has demonstrated the ability to increase platelet counts. This study will test the safety and efficacy of this investigational drug in the prevention of thrombocytopenia in patients with solid tumors, lymphomas or multiple myeloma who are receiving myelosuppressive treatment regimens requiring platelet transfusion support.