Riemann-based SPH method has shown strong potential for simulating multiphase flows with large density ratios and strong shock waves, but conventional formulations often suffer from excessive numerical dissipation and inaccurate pressure gradient approximation, especially in light phases and near highly deformable interfaces. In this work, an improved multiphase Riemann SPH method is developed to enhance accuracy while maintaining robustness under extreme flow conditions. A pressure differencing formulation (PDF) is employed for pressure gradient evaluation, providing higher-order consistency than the traditional pressure summation formulation. To suppress dissipation introduced by approximate Riemann solvers, a dissipation limiter is embedded into the solver, enabling adaptive activation only in compressive wave regions. In addition, a renormalization operator and a particle shifting technique are adopted to restore gradient consistency and preserve particle regularity, improving stability in strongly compressible multiphase flows. The method is validated using benchmark problems with strong discontinuities and large density contrasts. Results show reduced spurious pressure and velocity oscillations in the light phase, improved energy conservation, and sharper resolution of shocks and interfaces with reduced numerical damping. Application to underwater explosion bubble dynamics further demonstrates its capability in resolving complex multiphase interactions.