The eddy-preserving limiter has been demonstrated to outperform the conventional van Albada limiter for monotone upstream-centered schemes for conservation laws (MUSCL) for vortical flows. It reduces the dissipation by inactivating the conventional van Albada limiter in the interpolation of velocity components on the swirl plane of the vortex. In this work, we extend the limiter for the interpolation of pressure since a minimum pressure often exists along the axis of a free vortex. Three-dimensional vortex advection cases are employed to demonstrate the effects of the novel scheme. An extended eddy-preserving limiter scheme has been demonstrated to further improve the preservation of the pressure extrema. Finally, the scheme is applied to flow through a draft tube and the numerical results are compared against experimental data.