This work presents an extension of the elastic-corrector rate formulation—a novel framework for large strain elastoplasticity that preserves the multiplicative decomposition of the deformation gradient while avoiding the theoretical inconsistencies of Green-like strain decompositions or objective-rate hypoelasticity. Unlike traditional approaches, this hyperelasticity-based, weak-invariant framework is consistent across any stress-strain work-conjugate couple and remains unconstrained by the magnitude of elastic or plastic strains, making it equally applicable to metals and polymers. A key advantage of this formulation is its kinematic simplicity; large strain effects are reduced to a pre- and post-processor, even under conditions of both elastic and plastic anisotropy. While previous works have successfully addressed continuum anisotropy and nonlinear kinematic hardening, this study extends the framework to non-isochoric void-growth plasticity. Using the Gurson-Tvergaard-Needleman (GTN) yield function as a benchmark, we demonstrate that the formulation exactly preserves the kinematics of volumetric parts. This is particularly relevant for modeling porous materials such as cast or 3D-printed metals, foams, and metamaterials, where plastic flow in the matrix drives volume growth. We provide details on the implementation of a fully implicit algorithm that retains the efficient additive updates typical of infinitesimal formulations while remaining strictly consistent with finite strain hyperelasticity. The results confirm that the physical soundness and algorithmic simplicity of the elastic-corrector approach are maintained even when transitioning to complex, pressure-dependent constitutive models.