Capable constitutive modeling involves nonlinear and nonsmooth equation systems which are excessively demanding for traditional root solvers and established inelasticity algorithms. An example of difficult constitutive integration is provided by porous hyperelastic/plastic materials, such as polymers in additive manufacturing, (areias2025). In addition, gradient-enhanced damage and phase-field algorithms for fracture already make use of strongly coupled algorithms. Another example is crystal plasticity integration algorithms, which have to deal with its combinatorial character (areias2024). As extensions to our Lagrangian finite-strain plasticity framework based on the approximate exponential integrator, we introduce two new algorithms: i) a fixed-radius trust region root finder for the nonlinear system involving the elastic right Cauchy Green tensor and plastic multiplier ii) a partitioned approach for the hardening/porosity variables, which are determined in a staggered form using the strongly-coupled concept typically adopted for multiphysics problems. This allows the use of intricate hyperelastic laws combined with recent yield functions, which otherwise would involve a laborious treatment, and the use of corresponding work-hardening. Work-hardening would introduce significant nonlinearities in the constitutive system if used in a fully-coupled form. For the partitioned approach, a dynamic relaxation algorithm is adopted. This allows the efficient solution of the two nonlinear equations without significant drifting. Results show that robustness and efficiency are significantly improved. Significant testing is performed with imposed strains up to 100 for a carbon steel. This contributes to the robustness of equilibrium iterations. Drifting is also assessed as a function of number of steps in the dynamic relaxation algorithm.