We describe a code development and integration effort aimed at producing a numerical tool suitable for exploring the effects of stellar rotation and magnetic fields in a neutrino-driven core-collapse supernova environment. A one-dimensional, multi-energy group, flux-limited neutrino diffusion module (MGFLD) has been integrated with ZEUS-MP, a multidimensional, parallel gas hydrodynamics and magnetohydrodynamics code. With the neutrino diffusion module, ZEUS-MP can simulate the core-collapse, bounce, and explosion of a stellar progenitor in two and three space dimensions in which multidimensional hydrodynamics are coupled to 1-D neutrino transport in a ray-by-ray approximation. This paper describes the physics capabilities of the code and the technique for implementing the serial MGFLD module for parallel execution in a multi-dimensional simulation. Because the development and debugging of the integrated code is not yet complete, we provide a current status report of the effort and identify outstanding issues currently under investigation.