Spatial behavior of the stacking fault excitons (SFE's) excited heavily in a two-dimensional space at a stacking fault interface in BiI 3 has been studied. The SFE's whose center-of-mass motion is confined at the interface show more efficient spatial expansion for higher excitation densities. In order to get phase information of the high-density SFE masses, the degnerate four-wave-mixing (DFWM) measurements with two laser beams including space-resolved regime were performed. It was found that the increase in the dephasing due to exciton-exciton collision is suppressed above a certain density. In a space-resolved regime, it turned out that the high-density exciton mass excited at one laser spot propagates coherently to the other laser-spot propagates coherently to the other laser-spot site and induces nonlinear polarization resulting in momentum-selective emission of the DFWM lights. These result suggest the possibility of a coherent collective motion of the SFE masses in a new condensate of the high-density exciton-polaritons.