This study is to assess sorafenib as second treatment for patients that have previously received only sunitinib as first-line treatment for advanced renal cell cancer, and who either responded and then progressed with sunitinib or were intolerant to sunitinib. This study is to assess if combining the usual dose of sorafenib (200mg twice-daily) with low dose interferon (3 million international unit (MIU) five times a week) can treat kidney cancer more effectively than the current approved dose alone and if it is safe. In addition, for patients that respond to treatment with sorafenib alone or in combination with interferon before progressing, patients may receive sorafenib alone at an increased dose of 300mg twice-daily, provided that toxicities are acceptable and at the discretion of the investigator.