In this work, the Eulerian simulation of turbulent two-phase flows is investigated. In the case of high-Stokes number flows, the disperse phase can exhibit Particle Trajectory Crossings (PTC). Such complex dynamics can be captured by quadrature approaches like CQMOM (Yuan et al. 2011), which assume the velocity distribution to be a sum of Dirac's delta functions. In the context of Large Eddy Simulation (LES), the effect of the subgrid scales of the carrier phase on the disperse may be seen as a velocity dispersion. To extend quadrature approaches to LES, the Multi-Gaussian quadrature of Chalons et al. 2010 is envisaged. Such a method can account for PTC, by using several quadrature points, but can also capture the subgrid-scales-induced dispersion by means of a Gaussian distribution for each quadrature point. We also expect that this method is fully hyperbolic. This approach is evaluated with Direct Numerical Simulations on Taylor-Green vortices. Results show that the method avoids delta-shocks generated by the weakly hyperbolic system of CQMOM for high-Stokes Flows, and captures additional features in very high-Stokes number flows, where PTC between more than two trajectories are observed.