A system to induce remission in diseases characterized by excess production of soluble TNF receptors (sTNFR) and soluble interleukin 2 receptors (sIL2R) has been developed. In the most preferred embodiment, the system consists of antibodies to sTNFR1, sTNFR2 and sIL2R immobilized in a column containing a material such as Sepharose „¢ . The patient is connected to a pheresis machine which separates the blood into the plasma and red cells, and the plasma is circulated through the column until the desired reduction in levels of sTNFR1, sTNFR2 and sIL2R is achieved, preferably to less than normal levels. Preferably, patients are treated three times a week for four weeks, and this can be repeated after a period of time. Clinical studies showed reduction in tumor burden in patients having failed conventional chemotherapy and radiation treatments.