About 75% of US population living today will not die of cancer. There has been a recent report of a colony of cancer-resistant mice developed from a single male mouse that unexpectedly survived challenges of lethal cancer cell injections. In these so-called spontaneous regression/complete resistant (SR/CR) mice, cancer cells are killed by rapid infiltration of leukocytes, mainly of innate immunity. This highly effective natural cancer immunity is inherited and mediated entirely by white blood cells. Moreover, this cancer resistance can be transferred to wild type mice through the transfer of various immune cell types including granulocytes. The infusion of white blood cells, particularly cells of innate immunity, is a viable anticancer therapy in humans as well. This proposed trial will test whether white blood cell infusions from healthy unrelated donors can be used to treat cancer. The trial is designed to determine whether responses can be seen in cancer patients after infusion of HLA-mismatched white cells from healthy donors. It is important that the donors and recipients be unrelated and HLA-mismatched to avoid the possibility of transfusion-related Graft vs. Host Disease. The white blood cells from the healthy donors are being collected via apheresis following granulocyte mobilization with dexamethasone and filgrastim. The investigators will refer to the white blood cells as 'granulocytes' because 75-90% of the white blood cells collected through the apheresis will consist of granulocytes. The dose of at least 2x10 to the11th will be given from 4-5 donors at a rate of no more than one donor per day for each recipient. There will only be one infusion per day and no more than 5 infusions per week. Thus, a typical treatment in the study would span 1-2 weeks. After each infusion, the patients will be monitored carefully for possible adverse events. If adverse events occur at any time point during or after individual infusion, the treatment can be stopped until the adverse events can be managed. The daily dose of each infusion is a frequently used level that has a long safety record. The trial will observe the subject's cancer for 3 months after the granulocyte infusions are completed. Response at 90 days will be based on comparison of tumor measurements at baseline. The trial has 3 major endpoints: dose response and tolerance, safety, and efficacy.