This study is a single arm, pilot study of sirolimus in patient with Phosphatidylinositide-3-kinase (PIK3CA) mutation, PIK3CA amplification , PIK3CA-AKT pathway aberration Refractory solid tumor and/or specific sensitivity to mTOR inhibitors by Avatar scan that has progressed following standard therapy or that has not responded to standard therapy or for which there is no standard therapy.