Crystal Plasticity approaches that utilise a Lagrangian frame of reference in their mathematical formulation often struggle with large deformations and high strain rates, due to localised mesh distortion. This work presents a Eulerian formulation for modeling multiphase plasticity under extreme loading conditions, with applications to shock propagation and high strain and strain-rate deformation. The proposed approach integrates a crystal plasticity framework within a cell centered finite volume scheme to capture the deformation of heterogeneous microstructures and phase interactions. The finite volume approach is employed due to its inherent conservatism, which is beneficial during the advection of fields in the computational domain. Additionally a multi-phase diffuse interface representation of the microstructure is adopted. The model incorporates an extended constitutive formulation that captures strain hardening, rate dependence, and anisotropic behavior characteristic of polycrystalline aggregates. Benchmark simulations are conducted to verify the approach against analytical results before application to multiphase polycrystalline cases of interest. Figure \ref{3D_Laths} shows the application of the framework to an $\alpha$-$\beta$ Titanium microstructure under extreme deformation.