We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the 'tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a collection of cells accounting for the "waste" and/or dead cells in the presence of a nutrient. Here, the tumor is thought of as a growing continuum such that both the domain occupied but the tumor as well as it boundary evolve in time. The key characteristic of the present model is that the total density of cancerous cells is allowed to vary. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diusion, viscosity and pressure in the weak formulation, as well as convergence and compactness argument in the spirit of Lions.