Patients achieving at least a partial response after 12 courses may continue to receive CCI-779 and lenalidomide as above in the absence of disease progression. Cohorts of 3 patients receive escalating doses of CCI-779 until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 2 of 6 patients experience dose-limiting toxicity. Ten patients are treated at the MTD. Patients undergo blood sample and bone marrow collection periodically during study treatment for pharmacokinetic and pharmacodynamic studies, and to determine the immunomodulatory effects of CCI-779 and lenalidomide.