The recently established agreement between experiment and theory for the g factors of lithiumlike silicon and calcium ions manifests the most stringent test of the many-electron bound-state quantum electrodynamics (QED) effects in the presence of a magnetic field. In this Letter, we present a significant simultaneous improvement of both theoretical g_{th}=2.000 889 894 4 (34) and experimental g_{exp}=2.000 889 888 45 (14) values of the g factor of lithiumlike silicon ^{28}Si^{11+}. The theoretical precision now is limited by the many-electron two-loop contributions of the bound-state QED. The experimental value is accurate enough to test these contributions on a few percent level.