Compressible multiphase flows occur in a variety of engineering applications and have been an active area of research for decades. Models have been developed for both dilute and granular multiphase flows, but the regime between these states is not as well understood. We have developed a Lagrangian particle tracking methodology that studies this intermediate regime. Position and velocity are computed for spherical particles as a function of time while handling any collisions between them. Collisions are treated using a hard sphere model, where collisions are modeled as instantaneous impulsive forces. Energy losses are accounted for through restitution and friction coefficients. The particles are allowed to be mixed sizes and are not restricted to equal external accelerations. The results are validated by ensuring conservation of energy and momentum. This approach will be integrated with a computational fluid dynamics (CFD) solver to allow full two-way coupling between the solid and fluid phases. This will enable highly detailed studies of multiphase flows in the complex regime between dilute and granular flows.